Add the calculated WMClass to generated .desktop files.

chrome/browser/ui/gtk/browser_window_gtk.cc

Index: chrome/browser/ui/gtk/browser_window_gtk.cc
diff --git a/chrome/browser/ui/gtk/browser_window_gtk.cc b/chrome/browser/ui/gtk/browser_window_gtk.cc
index 1f984c4ef5218d38ad229995469c56d308192422..2b1d3f85b59e6cdd1925dcd4680f48be00be285c 100644
--- a/chrome/browser/ui/gtk/browser_window_gtk.cc
+++ b/chrome/browser/ui/gtk/browser_window_gtk.cc
@@ -70,6 +70,7 @@
 #include "chrome/browser/ui/tab_contents/tab_contents_wrapper.h"
 #include "chrome/browser/ui/webui/bug_report_ui.h"
 #include "chrome/browser/ui/window_sizer.h"
+#include "chrome/browser/web_applications/web_app.h"
 #include "chrome/common/chrome_switches.h"
 #include "chrome/common/pref_names.h"
 #include "content/browser/renderer_host/render_widget_host_view.h"
@@ -293,12 +294,12 @@ void BrowserWindowGtk::Init() {
   g_object_unref(gtk_window_get_group(window_));
 
   if (browser_->type() & Browser::TYPE_APP) {
-    std::string wmclassname = browser_->app_name();
-    if (wmclassname != DevToolsWindow::kDevToolsApp) {
-      file_util::ReplaceIllegalCharactersInPath(&wmclassname, '_');
-      TrimString(wmclassname, "_", &wmclassname);
-      gtk_window_set_wmclass(window_, wmclassname.c_str(),
-                             wmclassname.c_str());
+    std::string app_name = browser_->app_name();
+    if (app_name != DevToolsWindow::kDevToolsApp) {
+      std::string wmclassname = web_app::GetWMClassFromAppName(app_name);
+      gtk_window_set_wmclass(window_,
+                             wmclassname.c_str(),
+                             gdk_get_program_class());
     }
   }