We compute the total power operation for the Morava –theory of any finite group up to torsion. Our formula is stated in terms of the –action on the Drinfel’d ring of full level structures on the formal group associated to –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 –theory to –invariant generalized class functions is a natural transformation of global power functors on finite groups.
"The character of the total power operation." Geom. Topol. 21 (1) 385 - 440, 2017. https://doi.org/10.2140/gt.2017.21.385