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Thursday, February 19, 2015

**Abstract:** The total power operation in Morava E-theory is a mysterious map. It is multiplicative but not additive. It has deep algebro-geometric properties that have been studied by Ando, Hopkins, Rezk, and Strickland. The Morava E-theory of finite groups admits a character theory which approximates E(BG) by a form of ``generalized class functions" on the group. In this talk we construct a total power operation on generalized class functions that is compatible with the total power operation for Morava E-theory through the character maps of Hopkins, Kuhn, and Ravenel. This takes advantage of an intriguing connection between the Drinfeld ring of full level structures on a height n formal group and the conjugacy classes of commuting n-tuples in the wreath product of a finite group with a symmetric group.