Route through the BGTaskScheduler when receiving a message for the GCM Driver

chrome/android/java_sources.gni

 # Copyright 2016 The Chromium Authors. All rights reserved.
 # Use of this source code is governed by a BSD-style license that can be
 # found in the LICENSE file.
 
 chrome_java_sources = [
   "java/src/com/google/android/apps/chrome/appwidget/bookmarks/BookmarkThumbnailWidgetProvider.java",
   "java/src/org/chromium/chrome/browser/ActivityTabTaskDescriptionHelper.java",
   "java/src/org/chromium/chrome/browser/ActivityTaskDescriptionIconGenerator.java",
   "java/src/org/chromium/chrome/browser/AfterStartupTaskUtils.java",
   "java/src/org/chromium/chrome/browser/ApplicationInitialization.java",
@@ skipping 868 matching lines @@
   "java/src/org/chromium/chrome/browser/provider/SearchColumns.java",
   "java/src/org/chromium/chrome/browser/push_messaging/PushMessagingServiceObserver.java",
   "java/src/org/chromium/chrome/browser/rappor/RapporServiceBridge.java",
   "java/src/org/chromium/chrome/browser/rlz/RevenueStats.java",
   "java/src/org/chromium/chrome/browser/search_engines/TemplateUrlService.java",
   "java/src/org/chromium/chrome/browser/services/AccountsChangedReceiver.java",
   "java/src/org/chromium/chrome/browser/services/AndroidEduAndChildAccountHelper.java",
   "java/src/org/chromium/chrome/browser/services/AndroidEduOwnerCheckCallback.java",
   "java/src/org/chromium/chrome/browser/services/GoogleServicesManager.java",
   "java/src/org/chromium/chrome/browser/services/gcm/ChromeGcmListenerService.java",
+  "java/src/org/chromium/chrome/browser/services/gcm/GCMBackgroundTask.java",
   "java/src/org/chromium/chrome/browser/services/gcm/GcmUma.java",
   "java/src/org/chromium/chrome/browser/services/gcm/InvalidationGcmUpstreamSender.java",
   "java/src/org/chromium/chrome/browser/sessions/SessionTabHelper.java",
   "java/src/org/chromium/chrome/browser/shapedetection/BarcodeDetectionImpl.java",
   "java/src/org/chromium/chrome/browser/shapedetection/TextDetectionImpl.java",
   "java/src/org/chromium/chrome/browser/share/OptionalShareTargetsManager.java",
   "java/src/org/chromium/chrome/browser/share/ShareDialogAdapter.java",
   "java/src/org/chromium/chrome/browser/share/ShareHelper.java",
   "java/src/org/chromium/chrome/browser/signin/AccountAdder.java",
   "java/src/org/chromium/chrome/browser/signin/AccountIdProvider.java",
@@ skipping 714 matching lines @@
   "sync_shell/javatests/src/org/chromium/chrome/browser/sync/SyncTestBase.java",
   "sync_shell/javatests/src/org/chromium/chrome/browser/sync/TypedUrlsTest.java",
   "sync_shell/javatests/src/org/chromium/chrome/browser/sync/ui/PassphraseTypeDialogFragmentTest.java",
 ]
 
 # Only used for testing, should not be shipped to end users.
 if (!is_official_build) {
   chrome_java_sources += [ "java/src/org/chromium/chrome/browser/offlinepages/evaluation/OfflinePageEvaluationBridge.java" ]
   chrome_test_java_sources += [ "javatests/src/org/chromium/chrome/browser/offlinepages/OfflinePageSavePageLaterEvaluationTest.java" ]
 }