Graph C∗-algebras and z2-quotients of quantum spheres

We consider two Z2-actions on the Podleś generic quantum spheres. They yield, as noncommutative quotient spaces, the Klimek-Lesmewski q-disc and the quantum real projective space, respectively. The C∗-algebas of all these quantum spaces are described as graph C∗-algebras. The K-groups of the thus presented C∗-algebras are then easily determined from the general theory of graph C∗-algebas. For the quantum real projective space, we also recall the classification of the classes of irreducible ∗-representations of its algebra and give a linear basis for this algebra.