  We introduce and study natural two-parameter families of quantum groups
motivated on one hand by the liberations of classical orthogonal groups and on
the other by quantum isometry groups of the duals of the free groups.
Specifically, for each pair (p,q) of non-negative integers we define and
investigate quantum groups O^+(p,q), B^+(p,q), S^+(p,q) and H^+(p,q)
corresponding to, respectively, orthogonal groups, bistochastic groups,
symmetric groups and hyperoctahedral groups. In the first three cases the new
quantum groups turn out to be related to the (dual free products of) free
quantum groups studied earlier. For H^+(p,q) the situation is different: we
show that H^+(p,0) is isomorphic to the quantum isometry group of the
C*-algebra of the free group and it can be viewed as a liberation of the
classical isometry group of the p-dimensional torus.
