Subject: Question regarding equivariant K-theory. From: Nitu Kitchloo Date: Mon, 12 Feb 2007 22:49:54 -0800 (PST) Here is a somewhat simple question about Equivariant K-theory: Suppose I have a representation of a compact Lie gp G on a general Hilbert space H (which contains all its subrepresentations infinitely often but fails to contain all representations), what can I say about the equivariant K-theory spectrum K(H) modelled on the Fred.operators on H? There seems to be a map from K(H) to the standard equivariant K-theory spectrum. Does that split? I am mostly interested in the homotopy of S0 \smash_G K(H). Any information would be welcome. Nitu.