1.3 of [@Ph15] and a generalization of Definition 3.2 of [@Ph11] to nonabelian finite groups and not necessarily separable C\*-algebras, and then omit some of their assumptions. (See Definition \[D\_9719\_AppRep\_Phi\] and Definition \[D\_9731\_NonAbTrAppRep\].) Clearly, in the setting of abelian groups and simple separable unital C\*-algebras, approximate representability in the sense of Phillips (Definition 3.2 of [@Ph11]), approximate representability in the sense of Izumi (Definition 3.6(2) of [@Iz1]), approximate representability in the sense of Osaka and Teruya (Definition 3.4 of [@LO19]), and approximate representability in our sense (Definition \[D\_9719\_AppRep\_Phi\]) are the same. There is no apparent reason to believe that strict approximate innerness implies approximate representability. No examples seem to be known.

Also, we prove that if $G$ is a finite group, $A$ is an infinite-dimensional simple unital stably finite C\*-algebra, and $\alpha \colon  G \to {{\operatorname{Aut}}}(A)$ be a tracially strictly approximately inner action, then the radii of comparison of $A$ and the crossed product are related by $${{\operatorname{rc}}}(A) \leq {{\operatorname{rc}}}\big( {C^* (G, A, {\alpha})}\big).$$ Getting the reverse inequality is likely to be very difficult. When we further assume that $C^*(G, A, \alpha)$ is simple, then the radii of comparison of $A$, the crossed product, and the fixed point algebra are 