As an Australian all I want to say is... just use the .com address. Call the company 'groupon.com' Advertise the .com. It will work!
For example, when you go to www.apple.com.au it redirects you to www.apple.com/au and no one thinks anything of it.
So this is either silly, or it is about more than the domain name, and more about the trademark in use locally.