I am going through Sims - Étale groupoids and their $C^*$ algebras and at Lemma 3.1.4. the author says that $f^**f\in C_c(G^{(0)})$ is supported on $s(supp(f))$ and $(f^**f)(s(\gamma))=|f(\gamma)|^2$ for all $\gamma\in supp(f)$. He says that it follows from the convolution formula $$(f*g)(\gamma)=f(\alpha)g(\beta)$$

I couldn't see how. If $\gamma=\alpha\beta\in UV$ then $(f^**f)(\gamma)=f^*(\alpha)f(\beta)=\overline{f(\alpha^{-1})}f(\beta)$

I tried to think on the examples provided but they don't seem to be related. For example, Example 3.1.5 has a product that is not convolution.

Is there any reference that helps understand these computations?