Is the convolution algebra a *-algebra?

Question

Let $G$ be a finite abelian group with $n$ elements. Consider the convolution algebra $C^*(G) \subset l^2(G)$, with multiplication: $$(a * b )(g) = \frac{1}{n}\sum_{x\in G} a(x)b(g-x)$$ Is there a certain involution map $\phi: C^*(G) \rightarrow C^*(G)$ such that $\phi(\phi(a))=a$ and $\phi(ab)=\phi(b)\phi(a)$ (Such that $C^*(G)$ is a $*$-algebra)?