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Consider the wreath product $\Gamma = F\wr \mathrm{F_n} =\bigoplus_{\mathrm{F_n}}F\rtimes\mathrm{F_n}$, with $F$ a finite group and$\mathrm{F_n}$ the free group on $n$ generators. We study the Baum-Connesconjecture for this group. Our aim is to explicitly describe the Baum-Connesassembly map for $F\wr \mathrm{F_n}$. To this end, we compute the topologicaland the analytical K-groups and exhibit their generators. Moreover, we presenta concrete 2-dimensional model for $\underline{E} \Gamma$. As a result of ourK-theoretic computations, we obtain that $\mathrm K_0(\mathrm C^*_{\mathrmr}(\Gamma))$ is the free abelian group of countable rank with a basisconsisting of projections in $\mathrm C^*_{\mathrmr}(\bigoplus_{\mathrm{F_n}}F)$ and $\mathrm K_1(\mathrm C^*_{\mathrmr}(\Gamma))$ is the free abelian group of rank $n$ with a basis consisting ofthe unitaries coming from the free group.

K-theory and K-homology of the wreath products of finite with free groups