Abstract: We pull back paradoxical dynamical systems (e.g. hyperbolic groups acting on their Gromov boundary), to paradoxical decompositions of the acting group itself. This allows to show that whenever such groups admit a minimal amenable topologically free action on a compact Hausdorff space, the attached crossed product C*-algebra is classified by K-theoretic data. This is joint work with Eusebio Gardella, Julian Kranz, and Petr Naryshkin.