ABSTRACT

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

form

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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