and strict approximate innerness {#Sec_Approx_Innner}
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In this section, we first prove that approximate representability in the sense of Izumi and approximate representability in the sense of Phillips are the same in the setting of nonabelian finite groups. We then give the definition of strictly approximately inner actions of finite groups on unital C\*-algebras. Then we find a unital linear map from $C^*(G, A, \alpha)$ to $A$ which is an approximate homomorphism on finite sets and whose restriction to $A$ is the identity map. Also, we show that the map ${{\operatorname{W}}}(\iota) \colon {{\operatorname{W}}}(A) \to {{\operatorname{W}}}({C^* (G, A, {\alpha})})$ and the map ${{\operatorname{Cu}}}(\iota) \colon {{\operatorname{Cu}}}(A) \to {{\operatorname{Cu}}}({C^* (G, A, {\alpha})})$ which are induced by the inclusion map of $A$ in $C^*(G, A, \alpha)$ are injective. We further find a lower bound and an upper bound for the radius of comparison of $C^*(G, A, \alpha)$.

Let $A$ be a C\*-algebra. We denote the set of all bounded sequences in A with the supremum norm and pointwise operations by $l^{\infty} ({{\mathbb{Z}}_{> 0}}, A)$. Define $$c_0 ({{\mathbb{Z}}_{> 0}}, A)=\left\{ (a_n)_{n \in {{\mathbb{Z}}_{> 0}}} \in  l^{\infty} ({{\mathbb{Z}}_{> 0}}, A) \colon \lim_{n \to \infty} \| a_n \|=0  \right\}.$$ Clearly $c_0 ({{\mathbb{Z}}_{> 0}}, A)$ is an ideal 