Adobe AIR is 32bit, so if you want to install it on a 64bit Fedora 11 you will need to install the 32bit version of the required packages:
[root@local ~]$ yum install gnome-keyring.i586 rpm-libs.i586
--> Processing Conflict: GConf2-2.26.2-1.fc11.2.x86_64 conflicts GConf2-dbus
--> Finished Dependency Resolution
GConf2-2.26.2-1.fc11.2.x86_64 from installed has depsolving problems
--> GConf2 conflicts with GConf2-dbus
Error: GConf2 conflicts with GConf2-dbus
To solve it, install GConf2.i586: [root@local ~]$ yum install GConf2.i586
Then, download Adobe AIR from Adobe's website and install it:
[root@local ~]$ chmod +x AdobeAIRInstaller.bin
[root@local ~]$ ./AdobeAIRInstaller.bin