The K-theory of p -compact groups

Abstract

In this paper, we show that the p-adic K-theory of a connected p-compact is the ring of invariants of the Weyl group action on the K-theory of a maximal torus. We apply this result to show that a connected finite loop space admits a maximal torus if and only if its complex K-theory is \( \lambda \)-isomorphic to the K-theory of some BG, where G is a compact connected Lie group.