diff --git a/CHANGELOG.md b/CHANGELOG.md
index db92767b1..e5b523efc 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -215,6 +215,7 @@ and adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
 - In Rust, a call like `String::from("…")`, `Vec::from([…])` or `NonNull::from(x)` no longer links to your project's own `impl From<YourType> for String` (or for `Vec`, `NonNull`, …) unless what it passes is a `YourType`. A method call on a standard-library value, like `files.iter()` or `buf.extend(…)`, links to your trait's implementation for that type only where the trait is imported. Before, every `String::from("…")` call in dioxus's CLI linked to one such conversion, and tokio's `vec.iter()` calls to an internal trait's `Vec` impl. Re-index Rust projects after upgrading.
 - In Rust, a type alias, struct, enum or function declared without `pub` now links only from its own module and the modules inside it, and a name a `use` brings in from one of your workspace's crates, like `use tokio_test::task::spawn` or `use crate::error::Error`, links only to an item of that crate or of a crate it depends on. Before, a file's `use crate::Result` could link its `Result<…>` types to another module's private `type Result`, as in dioxus's CLI, and a call to an imported function could link to another crate's function of the same name, such as tokio's test `spawn(…)` calls to one in its examples, or to nothing because a private function of that name was in the way. Re-index Rust projects after upgrading.
 - In C++, every name a declaration lists now has the declaration's type, like `strings_found` in google/breakpad's `ByteBuffer symbols_found, strings_found;` or `data_` in a class's `Table *index_, *data_;`, so calls on it link to that class's methods. Before, only the first name had its type read, and a call on another name linked to nothing or to the class of an earlier variable with the same name.
+- In Kotlin, a call on a library type you import, like Jetpack Compose's `Modifier.pad()`, now links to the extension your project declares on that type (`fun Modifier.pad()`), when the calling file can see it: same package, or imported by name or with `.*`. The library type's own methods, like `Modifier.fillMaxSize()`, still never link to a project method that shares the name.
 
 ## [1.6.2] - 2026-10-03
 
diff --git a/__tests__/kotlin-extension-on-imported-type.test.ts b/__tests__/kotlin-extension-on-imported-type.test.ts
new file mode 100644
index 000000000..70660b6b4
--- /dev/null
+++ b/__tests__/kotlin-extension-on-imported-type.test.ts
@@ -0,0 +1,112 @@
+/**
+ * A Kotlin import from outside the project owns its name (#2196): after
+ * `import androidx.compose.ui.Modifier`, `Modifier.fillMaxSize()` is
+ * Compose's, never a project method that happens to be called `fillMaxSize`.
+ * But Kotlin lets the project extend that type — `fun Modifier.pad()`,
+ * indexed as `Modifier::pad` — and `Modifier.pad()` is that extension when
+ * the call site can see it: in its own package, or imported by name or `.*`.
+ * `fun Color.Companion.fromHex()` is called the same way, `Color.fromHex()`.
+ */
+import { describe, it, expect, afterAll, beforeAll } from 'vitest';
+import * as fs from 'fs';
+import * as os from 'os';
+import * as path from 'path';
+import { CodeGraph } from '../src';
+
+let root = '';
+let cg: CodeGraph;
+
+beforeAll(async () => {
+  root = fs.mkdtempSync(path.join(os.tmpdir(), 'cg-kotlin-ext-imported-'));
+  const files: Record<string, string> = {
+    'src/main/kotlin/app/ui/Ext.kt': `package app.ui
+
+import androidx.compose.ui.Modifier
+import androidx.compose.ui.graphics.Color
+
+fun Modifier.pad(): Modifier = this
+
+fun Modifier.hidden(): Modifier = this
+
+fun Color.Companion.fromHex(hex: String): Color = Color.Red
+`,
+    'src/main/kotlin/app/other/Box.kt': `package app.other
+
+class Box {
+    fun fillMaxSize(): Box = this
+}
+`,
+    'src/main/kotlin/app/gen/Gen.kt': `package app.gen
+
+import javax.lang.model.element.Modifier
+
+fun Modifier.keyword(): String = name
+`,
+    'src/main/kotlin/app/ui/Screen.kt': `package app.ui
+
+import androidx.compose.ui.Modifier
+import androidx.compose.ui.graphics.Color
+
+fun screen() {
+    Modifier.pad()
+    Modifier.fillMaxSize()
+    Color.fromHex("#fff")
+}
+`,
+    'src/main/kotlin/app/feature/Feed.kt': `package app.feature
+
+import androidx.compose.ui.Modifier
+import app.gen.keyword
+import app.ui.pad
+
+fun feed() {
+    Modifier.pad()
+    Modifier.hidden()
+    Modifier.keyword()
+}
+`,
+    'src/main/kotlin/app/settings/Settings.kt': `package app.settings
+
+import androidx.compose.ui.Modifier
+import app.ui.*
+
+fun settings() {
+    Modifier.hidden()
+}
+`,
+  };
+  for (const [rel, content] of Object.entries(files)) {
+    fs.mkdirSync(path.dirname(path.join(root, rel)), { recursive: true });
+    fs.writeFileSync(path.join(root, rel), content);
+  }
+  cg = await CodeGraph.init(root, { index: true });
+});
+
+afterAll(() => {
+  cg?.close();
+  if (root) fs.rmSync(root, { recursive: true, force: true });
+});
+
+/** `kind qualified-name` of every non-structural edge out of a file. */
+function edgesFrom(file: string): string[] {
+  const ids = cg.getNodesInFile(file).map((n) => n.id);
+  return cg
+    .getOutgoingEdgesFrom(ids)
+    .filter((e) => e.kind !== 'contains' && e.kind !== 'imports')
+    .map((e) => `${e.kind} ${cg.getNode(e.target)!.qualifiedName}`)
+    .sort();
+}
+
+describe('Kotlin: a project extension on a type an outside import names', () => {
+  it('is what a call on that type reaches from the same package; the type’s own members stay outside', () => {
+    expect(edgesFrom('src/main/kotlin/app/ui/Screen.kt')).toEqual([
+      'calls Color::fromHex',
+      'calls Modifier::pad',
+    ]);
+  });
+
+  it('is reached from another package only through an import of it, by name or `.*`', () => {
+    expect(edgesFrom('src/main/kotlin/app/feature/Feed.kt')).toEqual(['calls Modifier::pad']);
+    expect(edgesFrom('src/main/kotlin/app/settings/Settings.kt')).toEqual(['calls Modifier::hidden']);
+  });
+});
diff --git a/src/resolution/name-matcher.ts b/src/resolution/name-matcher.ts
index c77621fb2..61daad1ee 100644
--- a/src/resolution/name-matcher.ts
+++ b/src/resolution/name-matcher.ts
@@ -1798,6 +1798,29 @@ function isJavaOutsideImport(name: string, ref: UnresolvedRef, context: Resoluti
   return true;
 }
 
+/**
+ * `Modifier.pad()` after `import androidx.compose.ui.Modifier`: the type is
+ * outside the project, but Kotlin lets the project extend it. The call reaches
+ * a project extension on that type — `fun Modifier.pad()`, indexed as
+ * `Modifier::pad` — that the call site can see (its file, its package, an
+ * import of it by name or `.*`) and whose own file imports the same type.
+ * Compose's own `Modifier.fillMaxSize()` matches none and stays unlinked.
+ */
+function kotlinExtensionOnImportedType(ref: UnresolvedRef, context: ResolutionContext): ResolvedRef | null {
+  const call = /^(\w+)\.(\w+)$/.exec(ref.referenceName);
+  if (!call || ref.referenceKind !== 'calls') return null;
+  const binding = context.getImportMappings(ref.filePath, ref.language).find((m) => m.localName === call[1]);
+  if (!binding) return null;
+  const pkg = binding.source.slice(0, binding.source.lastIndexOf('.'));
+  const extensions = context.getNodesByQualifiedName(`${binding.exportedName}::${call[2]}`).filter((n) => {
+    if (n.kind !== 'method' || n.language !== 'kotlin' || !isKotlinTopLevelVisible(n, ref, context)) return false;
+    const scope = kotlinFileScope(n.filePath, context);
+    return scope.imports.has(binding.source) || scope.stars.has(pkg);
+  });
+  const chosen = extensions.length > 1 ? extensions.filter((n) => n.filePath === ref.filePath) : extensions;
+  return chosen.length === 1 ? { original: ref, targetNodeId: chosen[0]!.id, confidence: 0.9, resolvedBy: 'qualified-name' } : null;
+}
+
 /** Lua's global functions, and the test runner's: `local type = type` is the standard library's `type`. */
 const LUA_GLOBAL_FUNCTIONS: ReadonlySet<string> = new Set([
   'assert', 'error', 'ipairs', 'pairs', 'next', 'type', 'tostring', 'tonumber', 'setmetatable', 'getmetatable',
@@ -18867,10 +18890,11 @@ function matchReferenceInner(
 
   // `import java.lang.reflect.Field;` — the file's `Field` is the JDK's, never
   // a project class of that name (gson's production code bound it to a test's
-  // nested `ParameterizedTypesTest.Field`).
+  // nested `ParameterizedTypesTest.Field`). Only a Kotlin extension the
+  // project declares on that type is in the graph.
   if ((ref.language === 'java' || ref.language === 'kotlin') && ref.referenceKind !== 'imports' &&
       isJavaOutsideImport(ref.referenceName.split('.')[0]!, ref, context)) {
-    return null;
+    return ref.language === 'kotlin' ? kotlinExtensionOnImportedType(ref, context) : null;
   }
 
   // A symbolic name in a Scala type is a type (`F ~> G`) or a kind-projector