I'm running 12.04 Precise Pangolin, with Gnome 3, and it looks like my computer has some strange ideas when it comes to accented keys.
Without changing any of the settings, the results I get are strange and inconsistent:
AltGr + a = æ AltGr + e = e AltGr + u = ↓ AltGr + 2 = ² AltGr + n = n AltGr + g = ŋ AltGr + Shift + e = E AltGr + Shift + u = ↑ AltGr + [ then e = ë AltGr + [ then o/i/u/a = nothing - These are the methods I've tried to use to get umlauted characters AltGr + 2 = ² AltGr + Shift + 2 = ⅛ AltGr + Shift + 2 + o = ⅛Ø AltGr + 2 + o = ²ø
When I follow the instructions here https://help.ubuntu.com/11.04/ubuntu-help/tips-specialchars.html, and I set the compose key to be Right Alt, AltGr (which is the alt key to the right of the space bar) turns into a fully working regular alt key, and I cannot enter any special characters. Changing the "Key to choose third level" has no effect.
I would prefer to have the fully working accented character system, but I'd settle for just being able to get ß and the vowels with umlauts.