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K-theory for discrete groups. (English) Zbl 0685.46041
Operator algebras and application. Vol. 1: Structure theory; K-theory, geometry and topology, Pap. UK-US Jt. Semin., Warwick/UK 1987, Lond. Math. Soc. Lect. Note Ser. 135, 1-20 (1988).
[For the entire collection see Zbl 0668.00014.]
The “Baum-Connes conjecture” asserts the isomorphism of the geometric K-theory (introduced by the authors) for the action of a Lie group on a $$C^{\infty}$$-manifold with the K-theory of the crossed product $$C^*$$- algebra. The present note contains a report on the status of the conjecture in the particular case of a discrete group acting on a point.
Reviewer: J.Cuntz

##### MSC:
 46L80 $$K$$-theory and operator algebras (including cyclic theory) 18F25 Algebraic $$K$$-theory and $$L$$-theory (category-theoretic aspects) 46L55 Noncommutative dynamical systems