On equivariant Kasparov theory and Spanier-Whitehead duality

Suppose thatG is a second countable compact Lie group and thatA andB are commutativeG-C*-algebras. Then the Kasparov groupKK_*^G(A, B) is a bifunctor onG-spaces. It is computed here in terms of equivariant stable homotopy theory. This result is a consequence of a more general study of equivariant Spanier-Whitehead duality and uses in an essential way the extension of the Kasparov machinery to the setting of -G-C*-algebras. As a consequence, we show that if (X, x₀) is a based separable compact metricG-ENR (such as a smooth compactG-manifold) and (Y, y₀) is a based countableG-CW-complex then there is a natural isomorphism

Keywords:	KeywordHeading"  > and phrases Kasparov groups  equivariantKK-theory  Spanier-Whitehead duality  limits ofC*-algebras    /content/Q7774251657M0511/xxlarge963.gif"   alt="  sgr"   align="  BASELINE"   border="  0"  >-C*-algebras  pro-C*-algebras  equivariantK-theory
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