Snooker was invented in the 19th century by a Maharadsha in India, but the English officers liked it so much that they established it in Britain when they came back home.

Billiard dates back to the 13th century game of paillemaille, played in France, Italy and England. The successors of this game were already very popular at most European courts long before Snooker was invented.
Concerning inventions originating from India, one shouldn't forget tonic water...
Chinine, a medicine against Malaria, tasted so bitter that they added it to soda with lemon juice and sugar. Result: Tonic water.
And again, when people came home from India, they already got used to it and production in Britain started. Without that, no one would ever had the luck to enjoy Gin & Tonic.