8 JONATHAN ROSENBERG AND CLAUDE SCHOCHET
We proceed next to the study of K^(-;Z ), equivariant
K-theory mod n. We show that the ring of R(G)-linear homology
operations is the exterior algebra over R(G) on the Bockstein
element. Finally, we classify admissible multiplications; these
correspond to elements of R(G)$Z and (if n is odd) exactly one
of them is (graded) commutative.
We note that if G is a finite group of odd order then M.
Bokstedt (unpublished thesis [Bo]) has obtained a short exact UCT
sequence for KQ(X), where X is a finite G-CW-complex. These
results would seem to be orthogonal to our own, as R(G) is always
of infinite homological dimension if G is of finite order.
According to I. Madsen and M. Rothenberg [Mad], Bokstedt also has
results in the compact Lie case which are along the same lines as
our own. We have not seen these results.
We wish to thank the Mathematical Sciences Research
Institute for supporting us in 1984-5, during which time this
paper was completed. We are grateful to A. Wassermann for telling
us about Theorem 3.7 (ii).