I\'m not sure why \"https://stackoverflow.com/questions/18142763/is-it-possible-to-show-full-screen-activity-without-leaving-room-using-google-re\" was closed as \"off topic
I have edited BaseGameActivity.onStop() and have removed gamehelper.onStop(). So I stop gamesclient only in onDestroy. My game work perfectly also in background now.
Short answer: No.
Long answer: It's not possible because of the way the API is designed. Bruno has explained that several times. If the API were designed to allow you to retain state, sure. But Google made the decision not to go in that direction.
I don't see that the question is off topic, but you ARE asking for something counter to the API. That's just the way it works, and there's not much use asking why it's not possible.