“…The proof of Theorem 1.3 makes a fundamental use of the presence of strict comparison of projections in twisted group C * -algebras C * (Γ, σ) of finitely generated nilpotent groups Γ, which we show by relying on the paper [32]. The results in [32] are, however, also valid for virtually nilpotent groups, and it might be that a version of Theorem 1.3 is also valid for more general (classes of) groups of polynomial growth. For such an extension, several parts in our approach, among others, the explicitly constructed Hilbert C * -modules (Theorem 1.4) would require different arguments, while there are also several ingredients that do currently not have analogues for virtual nilpotent groups, among others, the existence of suitable representation groups [57].…”