Symmetries of hyperbolic 4-manifolds

In this paper, for each finite group $G$, we construct explicitly a non-compact complete finite-volume arithmetic hyperbolic $4$-manifold $M$ such that $\mathrm{I}\mathrm{s}\mathrm{o}\mathrm{m}M\cong G$, or ${\mathrm{I}\mathrm{s}\mathrm{o}\mathrm{m}}^{+}M\cong G$. In order to do so, we use essentially the geometry of Coxeter polytopes in the hyperbolic $4$-space, on one hand, and the combinatorics of simplicial complexes, on the other.