Let $G$ be a discrete group acting on a Hausdorff compact space $X$ and $U$ be the unitary group of $C(X)$, the algebra of continuous functions on $X$. In this paper we show that there exists a *-homomorpism that connect every groupoid algebra associated with the \'etale transformation groupoid $X \times G$ to the group algebra associated to the semi direct product $ U \rtimes G$. As consequences, the groupoid Banach algebra $\ell^{I}(X \times G)$ is amenable if the acting group $G$ is amenable. In the other hand, if $ G $ is finite then $\ell^{I}(X \times G)$ is hermitian.
