MUMBAI—India’s richest man is catapulting hundreds of millions of poor people straight into the mobile internet age.

Mukesh Ambani, head of Reliance Industries, one of India’s largest conglomerates, has shelled out $35 billion of the company’s money to blanket the South Asian nation with its first all-4G network. By offering free calls and data for pennies, the telecom latecomer has upended the industry, setting off a cheap internet tsunami that is opening the market of 1.3 billion people to global tech and retailing titans.

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