of $l^{\infty} ({{\mathbb{Z}}_{> 0}}, A)$. Then define $$A_{\infty} = l^{\infty} ({{\mathbb{Z}}_{> 0}}, A)/ c_0 ({{\mathbb{Z}}_{> 0}}, A).$$ We identify $A$ with the C\*-subalgebra of $A_{\infty}$ consisting of the equivalence classes of constant sequences. Let $\alpha \colon G \to {{\operatorname{Aut}}}(A)$ be an action of a finite group $G$ on a C\*-algebra $A$. We write $\alpha_{\infty} \colon G \to {{\operatorname{Aut}}}(A_{\infty})$ for the induced action.

The following definition is a generalization of the Definition 3.6(2) of [@Iz1] to nonabelian finite groups in terms of the sequence algebra. It was also pointed out by Izumi in Remark 3.7 of [@Iz1].

\[Izum\_Def\_app\_Rep\] Let $\alpha \colon G \to {{\operatorname{Aut}}}(A)$ be an action of a finite group $G$ on a unital C\*-algebra $A$. The action $\alpha$ is said to be approximately representable if there exists a unitary representation $w$ of $G$ in $A_{\infty}$ such that:

1.  $\alpha_{{\infty} g} (x) = w(g)x w(g)^*$ for all $x \in A$ and all $g \in G$.

2.  $\alpha_{{\infty} g} (w(h)) = w(ghg^{-1})$ for all $g, h \in G$.

The following is a generalization of the Definition 1.3 of [@Ph15] to nonabelian finite groups.

\[D\_9719\_AppRep\_Phi\] Let $A$ be a unital [C\*-algebra]{}, let $G$ be a finite group, and let ${\alpha}\colon G \to 