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be a Hausdorff, étale groupoid that is minimal and topologically principal. We show that
is purely infinite simple if and only if all the non-zero positive elements of
are infinite in
is a Hausdorff, ample groupoid, then we show that
is purely infinite simple if and only if every non-zero projection in
is infinite in
. We then show how this result applies to
-algebras. Finally, we investigate strongly purely infinite groupoid
We study conditions that will ensure that a crossed product of a C*-algebra by a discrete exact group is purely infinite (simple or non-simple). We are particularly interested in the case of a discrete non-amenable exact group acting on a commutative C*-algebra, where our sufficient conditions can be phrased in terms of paradoxicality of subsets of the spectrum of the abelian C*-algebra. As an application of our results we show that every discrete countable non-amenable exact group admits a free amenable minimal action on the Cantor set such that the corresponding crossed product C*-algebra is a Kirchberg algebra in the UCT class.
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