  The basic notions and results of equivariant KK-theory concerning crossed
products can be extended to the case of locally compact quantum groups. We
recall these constructions and prove some usefull properties of subgroups and
amalgamated free products of discrete quantum groups. Using these properties
and a quantum analogue of the Bass-Serre tree, we establish the K-amenability
of amalgamated free products of amenable discrete quantum groups.
