On the topological ranks of Banach ∗^*‐algebras associated with groups of subexponential growth

Let be a group of subexponential growth and a Fell bundle. We show that any Banach ‐algebra that sits between the associated ‐algebra and its ‐envelope has the same topological stable rank and real rank as . We apply this result to compute the topological stable rank and real rank of various classes of symmetrized twisted ‐crossed products and show that some twisted ‐crossed products have topological stable rank 1. Our results are new even in the case of (untwisted) group algebras.