This article investigates an explicit description of the Baum–Connes assembly map of the wreath product , where is a finite and is the free group on generators. In order to do so, we take Davis–Lück’s approach to the topological side which allows computations by means of spectral sequences. Besides describing explicitly the K-groups and their generators, we present a concrete 2-dimensional model for the classifying space . As a result of our computations, we obtain that is the free abelian group of countable rank with a basis consisting of projections in , and is the free abelian group of rank with a basis represented by the unitaries coming from the free group.
"K-theory and K-homology of finite wreath products with free groups." Illinois J. Math. 63 (2) 317 - 334, August 2019. https://doi.org/10.1215/00192082-7768735