Purely infinite partial crossed products

Let (A,G,α) be a partial dynamical system. We show that there is a bijective correspondence between G-invariant ideals of A and ideals in the partial crossed product A⋊α,rG provided the action is exact and residually topologically free. Assuming, in addition, a technical condition-automatic when A is abelian-we show that A⋊α,rG is purely infinite if and only if the positive nonzero elements in A are properly infinite in A⋊α,rG. As an application we verify pure infiniteness of various partial crossed products, including realisations of the Cuntz algebras On, OA, ON, and OZ as partial crossed products.