AF C^*-algebras from non-AF groupoids.

We construct ample groupoids from certain categories of paths, and prove that their C^*-algebras coincide with the continued fraction approximately finite dimensional (AF) algebras of Effros and Shen. The proof relies on recent classification results for simple nuclear C^*-algebras. The groupoids are not principal. This provides examples of Cartan subalgebras in the continued fraction AF algebras that are isomorphic, but not conjugate, to the standard diagonal subalgebras. [ABSTRACT FROM AUTHOR]