In this work, among other results we prove that if $S$ is a right amenable semigroup and $\varphi=\{T_s: s\in S\}$ is a (quasi) nonexpansive semigroup on a closed, convex subset $C$ in a strictly convex reflexive Banach space $E$ such that the set $F(\varphi)$ of common fixed points of $\varphi$ is nonempty, then there exists a (quasi) nonexpansive retraction $P$ from $C$ onto $F(\varphi)$ such that $PT_t=T_tP=P$ for each $t\in S$ and every closed convex $\varphi$-invariant subset of $C$ is also $P$-invariant. Moreover, if the mappings are also affine then $T_{\mu}$ [12] is a quasi contractive affine retraction from $C$ onto $F(\varphi)$, such that $T_{\mu}T_t= T_t T_{\mu}= T_{\mu}$ for each $t\in S$, and $T_{\mu}x \in \overline{co}\{ T_t x: t\in S\}$ for each $x\in C$; and if $R$ is an arbitrary retraction from $C$ onto $F(\varphi)$ such that $Rx \in \overline{co}\{ T_t x: t\in S\}$ for each $x\in C$, then $R=T_{\mu}$. It is shown that if $T_t$'s are $F(\varphi)$-quasi contractive then the results hold without the strict convexity condition on $E$.
