Yes you can set up a fully owned subsidiary in India. You may have to comply with FDI norms, RBI regulations, FEMA guidlines, Companies Act etc.
We are based in Delhi and specialise in setting up foreign entities in India. In case you need any assistance, please feel free to contact me at firstname.lastname@example.org. I will happy to share further information about the firm and similar projects handled by us for variety of clients.
Sonal Kumar Singh
M/s A.K Singh & Co.
(Advocates, Solicitors & Consultants)