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Just figured I'd save everyone some frustration when it comes to Dead Trigger 2. Unfortunately since it's not available on Google Play even with the xposed mod, it has to be sideloaded from another Android device. A tegra based device specifically. But even then the apk will refuse to install. After taking a look at the apk's androidmanifest.xml file I found it requires the Google Maps system library. After editing these permissions out and repacking the apk it installed fine and the game works perfectly. As with the original Dead Trigger you'll need a keyboard in order to properly map the controls on first run.
I got the game up and running but i can not press play. none of the buttons on the controller work, they mouse and keyboard combo (Lodgitech K400r) doesn't let me click play either.
Here is a quick video of the issue I did
http://www.youtube.com/watch?v=yYkbG5qnCKQ
You need to use a regular USB keyboard, not a wireless one, and press "enter" on the numpad on the far right of the keyboard. That will get you past the main menu, once you have started playing the first level press "esc" then use the keyboard's arrow keys and the "enter" button again to navigate the options menu so you can remap the controls for the OUYA.
LightyKD and patrickjd2000, i've figured out a work around for your situation. I encountered the exact same thing myself and after trying everything I could think of I used a Moga controller since Dead Trigger 2 was optimized for it and it brought up the text entry box whenever I clicked on it. The game is looking for specific keybindings for that text box thing which is weird. I guess worse comes to worst you could go buy a moga controller at walmart and then return it immediately afterwards.
One important thing I should mention, is if you have it installed and it's working fine, DO NOT uninstall, use directory bind, or mess with the apk in anyway. This will cause the bug that LightyKD, patrickjd2000, and myself encountered and you will need a moga controller to get it working.