Thanx, Erel. I cut a fragment (without websockets).
Works fine under Android 4.4 (native phone and in Android emulator).
But there are troubles in emulators of 4.1 - 4.3.
Probably, the reason is Google Play Services release.
In 4.4 - 12.5.21 (000300-189987672). Enough modern.
In 4.1 - 4.3 - 9.2.56 (030-124593566). And I am not able to update it.
Another strange moment. isGooglePlayServicesAvailable returns unexpected results (unlike 4.4)