  We develop a framework suitable for obtaining simplicity criteria for reduced
$C^*$-algebras of Hausdorff etale groupoids. This is based on the study of
certain non-degenerate $C^*$-subalgebras (in the case of groupoids, the
$C^*$-algebra of the interior isotropy bundle), for which one can control
(non-unique) state extensions to the ambient C*-algebra. As an application, we
give simplicity criteria for reduced crossed products of abelian $C^*$-algebras
by discrete groups.

Operator Algebras