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Displaying a different module for each group when they log in is not currently possible. The closest and by far the easiest way to achieve something along these lines is to create custom blocks and then set the permissions for each block.
For instance, when an ononymous user visits your site (or when someone isn't logged in), you can have a custom block that welcomes them and informs them that they are not logged in or that they can register along with additional information and maybe a small image. You would then set the group permissions to have only anonymous users see this block.
You could then create a second block that welcomes the user to your site with whatever content you feel your registered users might like to see. You would then set the permission to this particular block to registered users only. Your first block would dissapear when your users log in.
Right now, as you have probably noticed, you can set a different module for your start page, however, this is a global setting that will affect all users. If for instance you set your News module as your home page and do not allow anonymous users to see this module, they might get a blank page, or in most case, just an error when going to your site saying they do not have the permission to view. A first impression that people will not favour.
The sort of functionality you are asking may be possible in future versions of XOOPS, but I'm unqualified to answer that question with any degree of certainty. I do know that you can not set a module for your home page and not allow anonymous users to not see.
I hope this helps some. If I seem to be missing the point, let us know so that we can bettter understand what you are trying to achieve.