2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76692The twisted Connes-Moscovici higher index theorem is generalized to the case of good orbifolds. The higher index is shown to be a rational number, and in fact non-integer in specific examples of 2-orbifolds. This results in a non-commutative geometry model that predicts the occurrence of fractional quantum numbers in the Hall effect on the hyperbolic plane.47 pages, LatexDifferential GeometryHigh Energy Physics - TheoryFunctional Analysis58G11, 58G18, 58G25text