This is for research and development purposes only.
Installing Google PlayStore should be possible by using APK Mirror: http://www.apkmirror.com/apk/google-inc/google-play-store/
The basic steps are downloading the APK file and using the
adb install <app.apk> command to push the file on the board and install it.
The following instructions demonstrate how to install Firefox on the board. You can adjust it to your Google PlayStore situation:
1) Download the app
Firefox was ported to Android. Downloading the Firefox APK-file from Mozilla ensures somewhere, that the APK file is not malware.
More details and the download links can be found here:
2) Install the app
adb install <app.apk> command pushes the app on the device and installes it.
$ adb install fennec-46.0.multi.android-arm.apk
5326 KB/s (41968843 bytes in 7.694s)