Quantum semigroups generated by locally compact semigroups

Let $S$ be a subsemigroup of a second countable locally compact group $G$, such that $S^{-1}S=G$. We consider the $C^{\ast }$-algebra $C_{\delta }^{\ast }(S)$ generated by the operators of translation by all elements of $S$ in $L^2(S)$. We show that this algebra admits a comultiplication which turns it into a compact quantum semigroup. The same is proved for the von Neumann algebra $VN(S)$ generated by $C_{\delta }^{\ast }(S)$.