Please improve the Project Settings dialog box. There should be a separate interface for managing groups rather than only through the project-specific settings.
If I have added a group to a project to assign permissions and then want to remove that group from the project I cannot. I can only delete the group, which also deletes it from every other project I have used it on. That's kind of crazy.
Also if this one action (which appears to be removing the group from only that specific project or session) is going to delete the existence of that group and all the permission settings wherever it is used (basically a kill all button) there should definitely be an "are you sure" dialog box that pops up.