Power operations in K-theory completed at a prime

A. Baker

We describe the action of power operations on the p-completed cooperation algebras K^0K = K0(K)^p for K-theory at a prime p, and K^0KO = K0(KO)^2. These results are used to identify the K(1)-local homotopy type of some E∞ ring spectra obtained by killing elements of Hopf invariant 1. 

Tbilisi Mathematical Journal, Special Issue (HomotopyTheorySpectra - 2020), pp. 33-49