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We provide easily-verified necessary and sufficient conditions for a skewgroup ring, or more generally, a crossed product ring, to be an Azumayaalgebra. We use our results to show that (suitable localisations of) skew grouprings associated to the quantum Kleinian singularities introduced by Chan,Kirkman, Walton, and Zhang in [CKWZ16a] are Azumaya, and use this to show thatthese algebras are maximal orders. We also give a new proof of Auslander'sTheorem for quantum Kleinian singularities.

Azumaya skew group algebras and an application to quantum Kleinian singularities