I have always been fascinated by India, ancient India to be more precise. It holds a lot of interest to those of us from an Indo-European background because of the enormous similarities. Linguistically it is a gold mine for reconstructing ancient Indo-European languages.
The influence of Indian MAs on the CMAs is a much debated subject. It is obvious that there is some mixture of something going on, afterall Da Mo (Bodhidharma) came from India and brought some physical exercises with him. The tiger form that I know is from Sichuan and looks a lot like some Kalari forms.
I think that one of the problems people run into with subjects like influence from one region to another is that they do not account for waves of influence or things like regional proximity. Its Da Mo, Shaolin and nothing else. Well bagua is not a Shaolin art so where did it come from? And then there is our tiger form. Where did that come from? Questions that need answers I suspect.
Puitting aside India and China, just think of the spread of Hindic culture in the world. Angkor in Cambodia, Prambanan in Indonesia, this culture spread far and wide. It seems unlikely that its martial traditions, so beautifully preserved in the Mahabarata and Ramayana, would be left behind. The kingdoms of the Khmer and on Java were built with warfare and bloodshed.
I think, if we look with a properly critical eye, and can put aside any personal biases, we might very well find Indian martial influences in a lot of Asia.