The K-theory of crossed products

Part of the Oberwolfach Seminars book series (OWS, volume 36)


Crossed products for group actions yield many interesting C*-algebras. First we consider the case of crossed products by ℤ. Their K-theory is computed by the Pimsner-Voiculescu exact sequence [101]. We use crossed Toeplitz algebras to get it, following [33]. For crossed products by more general groups, there is a good guess for what the K-theory ought to be: this is the celebrated Baum-Connes conjecture. We discuss an alternative formulation of this conjecture, which is once again based on Toeplitz algebras.


Exact Sequence Compact Group Banach Algebra Compact Subgroup Compact Open Subgroup 
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© Birkhäuser Verlag AG 2007

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