TITLE: The K-Theory of $p$-compact groups

AUTHORS: A. Jeanneret
         Mathematisches Institut
         Sidlerstrasse 5
         CH-3012 BERN (Switzerland)/
         A. Osse
         Institut de Mathematiques
         Rue Emile Argand 11
         CH-2007 NEUCHATEL (Switzerland)
         
ABSTRACT: In this paper, we show that the $p$-adic K-theory of a 
connected $p$-compact is the ring of inavariants 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.