oh ok I just took a look at it, it's a new table and has no workflow so all you have to do really is modify the 2 UI Actions called 'Create User' and 'Reject'.
current condition is this:
current.state == "pending" && (gs.hasRole("admin") || gs.hasRole("user_admin"))
so user_admins also have the rights to do this but if you want another role of as you said a group do this:
current.state == "pending" && gs.isMemberOf('sys_id of your group in there');
Also you might need to check the ACLs on that user_registration_request to ensure those users can read/write to that table.
Alternatively you could just give that group the user_admin role and that's a much easier fix then?
