Use a navigation drawer
There are too much things in the action bar/menu, some of which are actually top-level activities (like Swap).
It may be better to move them to App drawer, maybe together with installed apps and updates (merged together as My apps).
I think only Search and Refresh should be in the action bar, like in Google Play.
This includes moving the About dialog to a fragment.
I understand this is gonna take a lot of time to implement.