We prove structure theorems for holomorphic correspondences realizing matings between pinched polynomial-like maps with connected Julia sets and Hecke groups (Fuchsian representations of free products C2 * Cn of cyclic groups of orders 2 and n). We show that such matings are generated by two-to-two subcorrespondences if and only if the maps are Chebyshev-like. We describe the dynamical behaviour of these matings in detail in the case n = 4 and we present a conjectured combinatorial description of the connectedness locus in parameter space in this case.