Let A be an infinite-dimensional stably finite simple unital C*-algebra, let G be a finite group, and let α G→ Aut(A) be an action of G on A which has the weak tracial Rokhlin property. We prove that if A has property (TM), then the crossed product A_α G has property (TM). As a corollary, if A is an infinite-dimensional separable simple unital C*-algebra which has stable rank one and strict comparison, α G→ Aut(A) is an action of a finite group G on A with the weak tracial Rokhlin property, then A_α G has stable rank one.
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Fang et al. (2024) studied this question.
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