Is there any way to specify a Group Policy only for the users who are members of a trusted active directory domain?
Any user policy that applies to them is going to come out of the domain their account is a member of, unless you're overriding user policy processing with loopback policy processing.
Computer policy is going to come from the domain that the computer they are logging-on to is a member of.
Are you thinking something like this? "When one of these users from domain ABC logs-on to one of the computers that is a member of domain XYZ I'd like to have certain group policy settings apply. When an ABC user logs-on to an ABC computer, though, I don't want those settings to apply. When an XYZ user logs-on to an XYZ computer, I don't want those settings to apply either."
If so, then there's no way with simple group policy to do what you're describing. You could mimic the functions of group policy with a script that checked the logon domain of the user, but running such a script in the context of the user would not permit changes to computer-specific settings.
Let me know how off-target I am with what you're asking, and I'll edit to answer your real question... (smile)
Evan was correct in his first sentence. Turning on the user group policy loopback processing, to "Merge", fixed this problem for me. I also had to enable "Allow cross-forest user policy and roaming user profiles".
Our situation: User in domain ABC logs on to computer in domain XYZ. I wanted user specific policies to be applied only in domain XYZ. The specific policy was to disable the shutdown/restart ability. Obviously don't want this to apply to computers in domain ABC (the users PC).
I created a new GPO in XYZ with the following settings: