Power operations in $K$-theory completed at a prime

Abstract

We describe the action of power operations on the $p$-completed cooperation algebras K^\vee_0 K = K_0(K)\sphat_p for $K$-theory at a prime~$p$, and K^\vee_0 KO = K_0(KO)\sphat_2.Comment: Version 6: final update, to appear in special issue of the Tbilisi Mathematical Journal on Homotopy Theory, Spectra, and Structured Ring Spectr