2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/95038We compute the C*-algebra generated by a group of composition operators acting on certain reproducing kernel Hilbert spaces over the disk, where the symbols belong to a non-elementary Fuchsian group. We show that such a C*-algebra contains the compact operperators, and its quotient is isomorphic to the crossed product C*-algebra determined by the action of the group on the boundary circle. In addition we show that the C*-algebras obtained from composition operators acting on a natural family of Hilbert spaces are in fact isomorphic, and also determine the same Ext-class, which can be related to known extensions of the crossed product.25 pages, no figuresOperator Algebras47B33 (primary), 20H10, 46L80, 47L80 (secondary)text