  We study the problem of determining when the reduced twisted group C*-algebra
associated with a discrete group G is simple and/or has a unique tracial state,
and present new sufficient conditions for this to hold. One of our main tools
is a combinatorial property, that we call the relative Kleppner condition,
which ensures that a quotient group G/H acts by freely acting automorphisms on
the twisted group von Neumann algebra associated to a normal subgroup H. We
apply our results to different types of groups, e.g. wreath products and
Baumslag-Solitar groups.
