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Christine Day has been acting as an adviser on retail strategy and collaborations with smaller brands

Adidas AG has hired Christine Day, the former chief executive of Lululemon Athletica Inc., ​as ​part of the German sportswear maker’s effort to improve its performance in the intensely competitive women’s athletic business.

Ms. Day, 53, who ran the boutique yoga-wear maker during a period of tremendous growth, has been acting as an adviser to Adidas on retail strategy and collaborations with smaller brands since the middle of last year. Adidas confirmed the hire.

Ms. Day said she initially “rebuffed” a few attempts by Adidas to reach out to her, saying she wasn’t looking for a consulting gig. But after connecting with an Adidas executive about a shared interest in healthy eating, Ms. Day, who is the full-time chief executive of frozen-food company Luvo Inc., said she came around to the idea of advising an athletic company, and formally signed on as a consultant in May of last year.

“I look at myself as a free agent,” she said. “I have a choice at this stage in my career to play for the love of the game.”

From her days at Lululemon, Ms. Day said she admired some offerings from Adidas, particularly its Stella McCartney line, but noticed there was work to be done.