Let $G$ - discrete group. Consider $C^*$-algebra $C^*_\gamma(G)\subset B(\ell^2(G))$ which is generated by operators $T_g:\delta_x \mapsto \delta_{gxg^{-1}}$ where $g\in G$. Are there some good properties of such group $C^*$-algebras? Is it true that if $G$ - inner amenable group then $C^*$-algebra $C^*_\gamma(G)$ belongs to the UCT-class?
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$\begingroup$ I don't know the answer to your questions, but perhaps this paper of Kaniuth and Markfort has references or results that could help? ams.org/mathscinet-getitem?mr=1184756 $\endgroup$– Yemon ChoiCommented Oct 27, 2016 at 15:04
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