The completion theorem in K-theory for proper actions of a discrete group, 
by Wolfgang Lueck and Bob Oliver

We prove a version of the Atiyah-Segal completion theorem for proper actions 
of an infinite discrete group G. More precisely, for any finite proper 
G-CW-complex X, K^*(EG times_G X) is the completion of K^*_G(X) with respect 
to a certain ideal. We also show, for such G and X, that K_G(X) can be defined 
as the Grothendieck group of the monoid of G-vector bundles over X.