The K-theoretical range of Cuntz-Krieger algebras

We augment Restorff's classification of purely infinite Cuntz-Krieger algebras by describing the range of his invariant on purely infinite Cuntz-Krieger algebras. We also describe its range on purely infinite graph C⁎-algebras with finitely many ideals, and provide 'unital' range results for purely infinite Cuntz-Krieger algebras and unital purely infinite graph C⁎-algebras.