App windows with ids should remember fullscreen state.

chrome/browser/ui/gtk/apps/native_app_window_gtk.cc

 // Copyright 2013 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.
 
 #include "chrome/browser/ui/gtk/apps/native_app_window_gtk.h"
 
 #include <gdk/gdkx.h>
 #include <vector>
 
 #include "base/message_loop/message_pump_gtk.h"
@@ skipping 193 matching lines @@
 
 gfx::Rect NativeAppWindowGtk::GetRestoredBounds() const {
   gfx::Rect window_bounds = restored_bounds_;
   window_bounds.Inset(-GetFrameInsets());
   return window_bounds;
 }
 
 ui::WindowShowState NativeAppWindowGtk::GetRestoredState() const {
   if (IsMaximized())
     return ui::SHOW_STATE_MAXIMIZED;
+  if (IsFullscreen())
+    return ui::SHOW_STATE_FULLSCREEN;
   return ui::SHOW_STATE_NORMAL;
 }
 
 gfx::Rect NativeAppWindowGtk::GetBounds() const {
   gfx::Rect window_bounds = bounds_;
   window_bounds.Inset(-GetFrameInsets());
   return window_bounds;
 }
 
 void NativeAppWindowGtk::Show() {
@@ skipping 396 matching lines @@
 }
 
 void NativeAppWindowGtk::UpdateDraggableRegions(
     const std::vector<extensions::DraggableRegion>& regions) {
   // Draggable region is not supported for non-frameless window.
   if (!frameless_)
     return;
 
   draggable_region_.reset(ShellWindow::RawDraggableRegionsToSkRegion(regions));
 }