Should I fast on the Day of Arafah and celebrate Eid al-Adha with the people of Saudi Arabia or with the Muslims of India?

If your country relies on moon sighting to determine the months, then Eid and the Day of Arafat will be according to what has been established by sighting in your country, not in Saudi Arabia. You fast on the Day of Arafat on the ninth day according to your sighting. It is permissible to fast on the day corresponding to Arafat in Saudi Arabia if it is not an Eid day in your country, because fasting is prescribed during the first ten days of Dhu al-Hijjah, with the exception of the Eid day.