If G is a compact connected Lie group with ?r1(G) torsion-free,
and if A and B are suitable C -algebras equipped with continuous
G-actions, then we construct a Kunneth spectral sequence of the
E* . = Tor*(G)(K^(A),KG(B)) =* KG(A0B),
where A$B is given the diagonal G-action. This generalizes the
Kunneth spectral sequence for equivariant K-theory of spaces, as
constructed by Hodgkin, Snaith, and McLeod. Then we construct a
Universal Coefficient spectral sequence
EP'* = ExtP(G)(K^(A),K^(B)) =* KKG(A,B)
for the equivariant Kasparov bivariant K-functor. We discuss
several applications, for instance to the question of determining
when G-algebras with K*(A) 3 K*(B) (as R(G)-modules) are
KK -equivalent.
1980 Mathematics Subject Classification (1985 Revision)
46L80, 46M20, 55U20, 55U25, 55N15, 55S25, 46L55.
Key words and phrases
Equivariant K-theory, Kunneth Theorem, Universal Coefficient
Theorem, Hodgkin spectral sequence, Pimsner-Voiculescu exact
sequence, Kasparov KK-functor, KK-equivalence, homology
operations, representation ring of a compact Lie group, actions
of compact groups on C -algebras.
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