Facebook OAuth on Google App Engine with iOS

I still have problems finding any tutorials to authenticate my native iOS application with OAuth 2 Facebook in the Google App Engine. I understand that I may need to use a proxy server in GAE (for example: Authentication with Google App Engine from Iphone Native Client ) to create a session with facebook, but what is the cleanest way to make SSO with facebook’s own user interface?

I would suggest that I will use something in accordance with the Facebook ios Auth instructions: http://developers.facebook.com/docs/tutorials/ios-sdk-tutorial/authenticate/

But how can I instead transfer the session to my GAE server and also cache the session on the client device so that it can authenticate https requests on my server? Basically I want to use simple-auth for GAE and the iOS app acts as its own (web client) (but does not use UIWebViews). Isn't there an easy way to do this?

By the way, I am using python in the Google App Engine. I found this for Java, but I honestly don't know what it does, because the documentation is not written yet http://www.lean-engine.com/index.html

Unanswered similar question: https://stackoverflow.com/questions/14878727/oauth-from-native-ios-app-with-oauth-from-facebook

EDIT: I basically want to have a login similar to Draw Something and other Zynga games, which allows users to simply use their own Facebook / iOS6 authentication to authenticate API calls on my server.

EDIT2: Found this informative post, but there is still no tutorial on how to do this Design for Facebook authentication in iOS app, which also accesses a secure web service