Yes, any NRIs (Non-resident Indians) can buy real estate either residential or commercial property in India. They do not require any special permission to purchase property and they can buy any number of real estate property based on their capacity. However, NRIs cannot buy agricultural land, plantation, or a farmhouse in India. They do not either acquire such property as a gift.
All real estate transactions are done by NRIs fall under the purview of FEMA (Foreign Exchange Management Act) and governed by the Reserve Bank of India.
NRIs can make payment through remittance from abroad into their regular Indian bank account or through the balance in the NRO or FCNR Account. They can similarly apply for a home loan as regular Indian home-buyer seeks a loan for buying the property. NRIs can give power of attorney to a person residing in India so that he/she can complete all formalities related to the acquisition of the property such as registration, possession, execution of an agreement of sale etc.