How to complete part of PhD in foreign lab but still get PhD from home insitution?
Some scholarships will pay for you to attend a foreign university for a short period of time as part of your PhD, which will give you the chance to work with a foreign researcher in their lab. For example, if you'd like to attend a university in the US, you could try for the Fulbright-Nehru Scholarship, which will allow you to spend 6-9 months at a U.S. host institute.