Reduced twisted group C*-algebras of groups with property P_PHP are completely selfless, and those of finite-by-G extensions have stable rank one and are pure.
Glasner,Proximal flows, Lecture Notes in Mathematics, vol
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Pureness and stable rank one for reduced twisted group $\mathrm{C}^\ast$-algebras of certain group extensions
Reduced twisted group C*-algebras of groups with property P_PHP are completely selfless, and those of finite-by-G extensions have stable rank one and are pure.