Nuvola Player is a Web Cloud Music Player for Linux. You can play Google Music using this application on most Linux. Nuvola Player runs web interface of cloud music service in its own window and provides integration with a Linux desktop (system tray, Ubuntu sound menu, dock menu and notifications). Currently supported services are Google Music, Grooveshark, Hype Machine and 8tracks.
Here are some screenshots of this Nuvola Player 2.3.3.