  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.
