This question comes up a lot. You can start a company in India or in US (or anywhere). That's basically same as investing in a company via stock market. You have ownership.
However, you cannot work for it while being in US on H1, even if it is based out of India. That will violate H1B's rules. I am not a lawyer, so cannot provide any legal advice, but this is what I found when I was looking into the same thing.
You can always do so however make sure the company is not in your own name :)
Great. Thank you so much guys for your answers. :)