India, Aug. 2 -- It took a World Cup to transform a remote cluster of islands that's home to more sheep than people into a cultural juggernaut.

A decision by Argentina's players to unfurl a banner about the disputed Falkland Islands after defeating England in the World Cup semifinals carried a historical cause onto the T-shirts, bedroom walls and Instagram feeds of a new generation. In the weeks since, the image that has endured from the tournament in soccer-crazed Argentina hasn't been of Lionel Messi. It's been the crudely painted sign reading: "The Malvinas are Argentine."

The South Atlantic archipelago, known in Argentina as the Malvinas, is claimed by both Argentina and Britain, which fought a 10-week war over the territory in 1982...