I think there's something wrong with my AirPods. I recently got it on a business trip to Japan, now I'm back to India. Can I get it checked under warranty at a local Apple Store?
There have been historical exceptions in the past such as with iPhone, where USA devices on CDMA networks were not serviceable outside the USA because they didn't work outside the USA and so the parts were not held by Apple in non US stores.
Typically however all Apple products have an international warranty in countries where Apple sells products, i.e. during the Iranian embargo any product brought into the country would not be serviceable because Apple doesn't service them.
However Apple does service products in India by the looks of it, so this shouldn't be an issue, you can call Apple Support to save a trip to an Apple Store.
You can also check warranty status online: https://checkcoverage.apple.com/