  In this paper, we consider the Wiener Hopf algebra, denoted
$\mathcal{W}(A,P,G,\alpha)$, associated to an action of a discrete subsemigroup
$P$ of a group $G$ on a $C^{*}$-algebra $A$. We show that
$\mathcal{W}(A,P,G,\alpha)$ can be represented as a groupoid crossed product.
As an application, we show that when $P=\mathbb{F}_{n}^{+}$, the free semigroup
on $n$ generators, the $K$-theory of $\mathcal{W}(A,P,G,\alpha)$ and the
$K$-theory of $A$ coincides.
