I am an Indian Citizen residing in India. Can I invest in an S&P500 Index fund while residing in India?
Can I invest in S&P500 Index fund, while residing in India
You can invest in US funds. Under the Liberalized Remittance Scheme one can invest up to USD 250,000 per year.
Open an account with an international broker. This is time consuming and KYC etc would take time. Transferring funds will also involve a bit of paperwork. You can then invest into a range of funds that track the S&P 500.
Open an Account with an Indian broker [or with AMFI]. There are quite a few fund houses that offer funds that invest in US markets; for example ICICI, Franklin, Motilal Oswal, DSP Blackrock, Birla Sunlife, etc. Most of these invest in a broad range of equity. Motilal has NASDAQ 100; it has filed a prospectus for S&P.
This would be more convenient in terms of KYC or depositing / withdrawing as your interaction will be with the Indian fund house.
There are 2 aspects to your questions as I perceive it. Whether or not you are eligible to invest in it as a non-US resident and whether or not you have access to it outside the US.
The short answer to both is yes.
You're perfectly fine to invest in USA based ETFs as a non-resident. The second part I cannot help directly with since I'm not based in India but for instance, in the EU, you can open local broker accounts to invest in cross-continent ETFs or skip that altogether and invest in ETFs and similar financial products through a robo-advisor (like Moneyfarm, Scalable, ETFmatic etc).
I'm fairly certain that for a big market like India you should be able to find someone offering broker accounts and/or robo-advisor options that include USA ETFs.
Charles Schwab, DriveWealth, Interactive Brokers, and a few others allow non resident aliens (not US citizen) that aren't active stock traders (i.e. only a few transactions every month) to open accounts with them.
Personally I find DriveWealth (you can sign up here) to be the most accessible one, due to not having any minimum balance and having low fees ($2.99 per transaction). They only charge a one-time $5 fee to file the W-8BEN tax form for you.
You can search for them and easily find coupons/referral codes that even give you $5 in Google stock for free when you sign up.
Further reading about this subject: How non-US citizens can invest in the US stock market?