  Given a self-similar groupoid action $(G,E)$ on a finite directed graph, we
prove some properties of the corresponding ample groupoid of germs $\mathcal
G(G,E)$. We study the analogue of the Higman-Thompson group associated to
$(G,E)$ using $G$-tables and relate it to the topological full group of
$\mathcal G(G,E)$, which is isomorphic to a subgroup of unitaries in the
algebra $C^*(G,E)$. After recalling some concepts in groupoid homology, we
discuss the Matui's AH-conjecture for $\mathcal G(G,E)$ in some particular
cases.
