Titel: "Group actions on compact and locally compact spaces and their C-algebras" Kirchberg and Phillips proved in the mid 1990’s that the socalled Kirchberg C-algebras are classified by K-theory. In a joint work with Sierakowski we proved that every exact and non-amenable countable discrete group 􀀀 admits a free minimal amenable action on the Cantor set X such that C(X) ored 􀀀 is a Kirchberg algebra. The proof relies on properties of the Roe algebra `1(􀀀) o 􀀀 and Tarski’s characterization of paradoxical sets in a group. For the similar result for actions on a non-compact locally compact Hausdorff space one needs to consider the so-called supramenable groups, which are groups that contain no paradoxical subset. We show that every (exact) non-supramenable group admits a free minimal amenable action on the locally compact non-compact Cantor set such that the crossed product is a (non-unital) Kirchberg algebra. This is a part of an ongoing joint work with Kellerhals and Monod.