#### Volume 21, issue 1 (2017)

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The character of the total power operation

### Tobias Barthel and Nathaniel Stapleton

Geometry & Topology 21 (2017) 385–440
##### Abstract

We compute the total power operation for the Morava $E$–theory of any finite group up to torsion. Our formula is stated in terms of the ${GL}_{n}\left({ℚ}_{p}\right)$–action on the Drinfel’d ring of full level structures on the formal group associated to $E$–theory. It can be specialized to give explicit descriptions of many classical operations. Moreover, we show that the character map of Hopkins, Kuhn and Ravenel from $E$–theory to ${GL}_{n}\left({ℤ}_{p}\right)$–invariant generalized class functions is a natural transformation of global power functors on finite groups.

##### Keywords
power operations, generalized character theory, Morava $E$–theory
##### Mathematical Subject Classification 2010
Primary: 55N22, 55S25
Secondary: 55P42