Yes, Non-Resident Indians (NRIs) are allowed to invest in the Indian stock market. They can do so through a Non-Resident External (NRE) account or a Non-Resident Ordinary (NRO) account. NRE accounts are for holding foreign-earned income, while NRO accounts are for holding income earned in India. NRIs can also invest in the Indian stock market through the Portfolio Investment Scheme (PIS) of the Reserve Bank of India (RBI), which allows them to purchase and sell shares on the Indian stock exchanges through a designated bank.