How can I implement GCM push notifications in AIR?

You have 2 ways, first is buy the ane, are alot such as: http://myappsnippet.com/gcm/ or review the open in: https://github.com/freshplanet/ANE-Push-Notification or http://afterisk.wordpress.com/2012/09/22/the-only-free-and-fully-functional-android-gcm-native-extension-for-adobe-air/ , that for client side, for server side you can buy in http://urbanairship.com/ or enter in the world of build your own pisblisher server, in this case you need to read android and ios and blackberry notification, each one has different methods.

Also, here you have more information: http://forums.adobe.com/message/4626292

looks good.