Some Permanence properties for crossed products by compact group actions with the tracial Rokhlin property

Abstract: In this paper, we give some properties of the fixed point algebra and the crossed product of a unital separable simple infinite dimensional C*-algebra by an action of a second-countable compact group with the tracial Rokhlin property with comparison that could be deduced from the properties of its original algebra: (1) stable rank one; (2) real rank zero; (3) $\beta$-comparison; (4) Winter's $n$-comparison; (5) $m$-almost divisible; (6) weakly ($m$,$n$)-divisible.