W’S FASHION FIX: The W Hotel chain’s fashion immersion continues to deepen. After 13 years of hosting a backstage lounge at the tents at Bryant Park during fashion week, the hospitality chain will next month sponsor the presentations of Monique Péan, Bibhu Mohapatra, Sophie Theallet and Rebecca Moses at the 125-person Box at Lincoln Center. Each designer has agreed to a season-long partnership with W that will include trunk shows at hotels around the world, creating items for W’s Global Glam fashion brand for spring and designing uniforms for new hotels. W’s global fashion director, Amanda Ross, tapped Behnaz Sarafpour, Fallon, Kara Ross, Minnie Mortimer, Olivia Harris, Duro Olowu, Christys of London, Roberta Freymann, Simone, Melissa Obadash, Lulu Frost, Saga Furs and Gigi Mortimer for Global Glam’s third season, winter-resort. Like previous Global Glam collections, designers were asked to use newly opened or soon-to-open W hotels as inspiration. W London in Leicester Square inspired Ross’ pocket that doubles as a leather pendant. W St. Petersburg elicited Saga Furs’ reversible mink muff with leather lining and Sarafpour’s jewelry made from gold silk thread. W Retreat and Spa, Vieques Island, conjured a bright yellow bikini for Obadash and tortoise shell sunglasses with coral-colored bamboo arms for Jennifer Creel. The collection is priced from $50 to $650 and available at W Hotels The Store. W will present the latest Global Glam collection on Sept. 12 at the Box at Lincoln Center, a spokeswoman said.