  We examine the question of quasidiagonality for C*-algebras of discrete
amenable groups from a variety of angles. We give a quantitative version of
Rosenberg's theorem via paradoxical decompositions and a characterization of
quasidiagonality for group C*-algebras in terms of embeddability of the groups.
We consider several notable examples of groups, such as topological full groups
associated with Cantor minimal systems and Abels' celebrated example of a
finitely presented solvable group that is not residually finite, and show that
they have quasidiagonal C*-algebras. Finally, we study strong quasidiagonality
for group C*-algebras, exhibiting classes of amenable groups with and without
strongly quasidiagonal C*-algebras.
