MYSORE, India — Thousands of Indians report to Infosys Technologies’ campus here to learn the finer points of programming. Lately, though, packs of foreigners have been roaming the manicured lawns, too.

Many of them are recent American college graduates, and some have even turned down job offers from coveted employers like Google. Instead, they accepted a novel assignment from Infosys, the Indian technology giant: fly here for six months of training, then return home to work in the company’s American back offices.

India is outsourcing outsourcing.

One of the constants of the global economy has been companies moving their tasks — and jobs — to India. But rising wages and a stronger currency here, demands for workers who speak languages other than English, and competition from countries looking to emulate India’s success as a back office — including China, Morocco and Mexico — are challenging that model.

Many executives here acknowledge that outsourcing, having rained most heavily on India, will increasingly sprinkle tasks around the globe. Or, as Ashok Vemuri, an Infosys senior vice president, put it, the future of outsourcing is “to take the work from any part of the world and do it in any part of the world.”