Purely infinite simple C⁎-algebras that are principal groupoid C⁎-algebras

From a suitable groupoid G  , we show how to construct an amenable principal groupoid whose C⁎C⁎-algebra is a Kirchberg algebra which is KK  -equivalent to C⁎(G)C⁎(G). Using this construction, we show by example that many UCT Kirchberg algebras can be realised as the C⁎C⁎-algebras of amenable principal groupoids.