One Indian magazine outlined the Indian Government's options: (1) All Tibetans who reach India automatically get refugee recognition. The Karmapa could thus be given de facto refugee status even if he didn't formally apply for political asylum. (2) If invited, he could go to a third country. In this case he would need an Indian Travel Document issued by New Delhi. It is not clear how the Chinese Government would react to the granting of such a document. (3) India could deny Beijing and grant him official refugee status following an application for political asylum.
This last scenario is clearly out of the question. The cost to India in relations with their northern neighbor would be too high. The second scenario is considered unlikely as the Karmapa has expressed his intention to remain in India. An invitation from the US not withstanding, his teachers are in India and it is there that he chooses to stay.
The first scenario appears the most likely. But analysts say there's no way the Karmapa can be termed an ordinary refugee. It's not clear how the Chinese authorities would react to this scenario either.
The bottomline is that the Chinese Government is calling for the Karmapa's return to Tibet. This is an obvious fourth option but the Indian press wasn't talking about it. It was widely ignored a a non-option.