* Kinnevik shares almost tripled during tenure
* Stock extends recent slide on concern over fashion firm
* Investment firm shifts focus to technology, e-commerce
* Brunell to stay on as director of key Kinnevik firms
* Zalando declines comment on Brunell's future role
By Helena Soderpalm and Mia Shanley
STOCKHOLM, Jan 22 (Reuters) - Mia Brunell is stepping down as chief executive of Swedish investment firm Kinnevik to seek a new challenge after eight years helping to transform the company into a leading investor in technology and e-commerce.
Brunell, who joined Kinnevik in 1992 and was CEO since August 2006, will stay in her role until a successor is appointed and will continue to be involved even after that, staying as a director of four companies the group invests in.
Founded in 1936, Kinnevik grew to become one of the largest listed investment companies in Europe with a market capitalisation of 73.9 billion Swedish crowns ($11.4 billion). It is controlled by Sweden's wealthy Stenbeck family.
Kinnevik's share price has nearly doubled in the past year as investors sought to boost their exposure to Europe's fast-growing online retail market.
Kinnevik has a 37 percent stake in Europe's biggest online fashion firm, Zalando, which started with shoes five years ago and now sells 1,500 different brands of clothes and accessories.
The Berlin-based retailer is viewed as a prime candidate for a listing this year and goes head-to-head with Britain's ASOS , whose share price is up 170 percent in the past year.
The Zalando investment is part of Kinnevik's shift towards e-commerce, telecommunications and media under Brunell and chairman Cristina Stenbeck, and away from investments in traditional Swedish industries such as paper and steel.
"I'm extremely proud and I'm pleased with the development we have - we have the strongest-ever financial position," Stenbeck told Reuters, pointing to recent divestments such as the Russian assets of telecoms operator Tele2 and packaging firm Billerudkorsnas.
Investments in e-commerce businesses such as Zalando, Russia's Lamoda, Home24 and Zalora in Southeast Asia - all start-ups launched by German venture capital firm Rocket Internet - make up about 30 percent of the group's overall portfolio.
Kinnevik shares had almost tripled since Brunell, a 48-year-old mother of two, took over in 2006, and were down 1.6 percent on the news she was stepping down, compared with a 0.3 percent rise in the broader Stockholm blue-chip bourse .
That extends a sharp fall in the stock which started last week following reports that suggested growth was slowing at Zalando at the end of 2013.
Stenbeck said she would favour an internal candidate to replace Brunell, but she might also look outside the group.
Kinnevik said Brunell would continue to be involved in the group in her roles as director of telecoms firms Tele2 , Millicom, online retail specialist CDON Group and media firm Modern Times Group.
Zalando changed its structure last month to one typically used by German listed companies and appointed Brunell as chair of a new six-person supervisory board. Zalando declined to comment on whether Brunell would be staying on the board.