  We give a decomposition of the equivariant Kasparov category for discrete
quantum group with torsions. As an outcome, we show that the crossed product by
a discrete quantum group in a certain class preserves the UCT. We then show
that quasidiagonality of a reduced C*-algebra of a countable discrete quantum
group $\Gamma$ implies that $\Gamma$ is amenable, and deduce from the work of
Tikuisis, White and Winter, and the results in the first part of the paper, the
converse (i.e. the quantum Rosenberg Conjecture) for a large class of countable
discrete unimodular quantum groups. We also note that the unimodularity is a
necessary condition.
