Coupon site Groupon Inc. filed today to sell $540 million in an initial share offer, far less than it had earlier anticipated after a series of stumbles and questions about its business model.

The  largest online-coupon site would be valued at $11.4 billion, down from the $25 billion the Chicago-based company had discussed with its bankers earlier this year, before the markets swooned because of the European debt crisis.

In a regulatory filing, Groupon said it will offer 30 million Class A shares at $16 to $18 each. In June, a filing showed it was planning to raise $750 million.

Investors might not be so keen to buy the shares, however. Although Groupon had sales of $430 million in the third quarter, those sales grew at 9.6 percent, a third the rate of the previous quarter.  Its losses fell to $10.6 million from a loss of $101.2 million in the prior quarter.

It might be several weeks before the shares start trading on the Nasdaq. Under U.S. regulatory rules, the company isn’t allowed to comment about its prospects before the share offering.

Facebook and dozens of other sites have moved into the online coupon business and many store owners have complained that the discount coupons don’t generate loyal customers.

Margo Georgiadis, Groupon’s chief operating officer, announced last month that he was returning to Google Inc. after five months at the increasingly embattled company.