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Jana Partners disclosed Friday that it has bought a major stake in Bellevue-based Outerwall and could push for a sale of the business.

The activist hedge fund said in a regulatory filing that it holds nearly 3.8 million shares in Outerwall, which used to be known as Coinstar. That represents a 13.5 percent stake in the company and makes it Outerwall’s largest shareholder.

Outerwall operates Redbox DVD rental kiosks and Coinstar coin-counting machines. It recently added a new ecoATM business, a self-serve kiosk system that buys back and recycles used mobile phones, tablets and other electronics.

Jana Partners said in the filing that it believes Outerwall’s shares are undervalued and it plans to meet with the company to discuss its strategic alternatives, including cost-cutting opportunities, a sale of the company or discontinuation of certain businesses.

Jana is seeking a sale or spinoff of two new Outerwall operations: its Rubi coffee kiosks and Redbox Instant, Bloomberg News reported, citing a person with knowledge of the situation who asked not to be identified.

Outerwall operates Rubi coffee-vending machines in supermarkets, drugstores and big-box outlets in a partnership with Starbucks-owned Seattle’s Best Coffee. Redbox Instant is a streaming-video service, started by Outerwall and Verizon Communications in March, which hasn’t yet developed into a credible threat to Netflix or

Outerwall said in a statement that it “welcomes the opinions of its shareholders and is always open to constructive input.”

The company said its leadership regularly reviews its strategic priorities and options. It also said that it will “continue to take actions” to drive value for all of its shareholders.

Outerwall changed its name from Coinstar in July and recently cut its third-quarter and full-year guidance due to the impact of price discounts on its performance.

Jana is run by Barry Rosenstein and has investments in a number of other companies including Boeing, online deal provider Groupon and retailer Office Depot. The firm declined to comment further.

Outerwall shares soared $4.92, or 9.4 percent, to close Friday’s regular trading session at $57.10. They jumped an additional $4.83, or 8.5 percent, to $61.93 in after-hours trading. The stock peaked year-to-date with a $65.30 close in July.

Information from Bloomberg News and Seattle Times archives is included in this report.