Polynomial growth and rapid decay on the dual of a bicross product

The bicrossed product construction is an efficient way of producing many non-trivial quantum groups with various interesting properties. The rapid decay property (property (RD)), first proposed by P. Jolissaint for groups and later generalized by R. Vergnioux to discrete quantum groups, is one particularly interesting approximation property due to its connection to K-theory.  My talk will focus on the permanence of the property (RD), and the closely related notion of polynomial growth, under the bicrossed product construction. If time permits, I will give some examples of compact bicrossed products whose dual has property (RD) but does not have polynomial growth.