  Connectivity is a homotopy invariant property of a separable C*-algebra A
which has three important consequences: absence of nontrivial projections,
quasidiagonality and realization of the Kasparov group KK(A,B) as homotopy
classes of asymptotic morphisms from A to the stabilization of B if A is
nuclear. Here we give a new characterization of connectivity for separable
exact C*-algebras and use this characterization to show that the class of
discrete countable amenable groups whose augmentation ideals are connective is
closed under generalized wreath products. In a related circle of ideas, we give
a result on quasidiagonality of reduced crossed-product C*-algebras associated
to noncommutative Bernoulli actions.
