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Generalized cluster algebras from orbifolds were defined by Chekhov andShapiro to give a combinatorial description of their Teichm\"uller spaces. Onecan also assign a gentle algebra to a triangulated orbifold, as in the work ofLabardini-Fragoso and Mou. In this work, we show that the Caldero-Chapoton mapand the snake graph expansion map agree for arcs in triangulated orbifolds andarc modules, and similarly for closed curves and certain band modules. As aconsequence, we have a bijection between some indecomposable modules over agentle algebra and cluster variables in a generalized cluster algebra whereboth algebras arise from the same triangulated orbifold.

Snake Graphs and Caldero-Chapoton Functions from Triangulated Orbifolds