  We observe that the von Neumann envelope of the quantum algebra of functions
on the normalizer of thegroup $\SU(1,1)\cong \SL(2,\mathbb R)$ in
$\SL(2,\mathbb C)$ via deformation quantization contains the von Neumann
algebraic quantum normalizer of $\SU(1,1)$ in the frame work of
Waronowicz-Korogodsky. We then use the technique of reduction to the maximal
subgroup to compute the K-theory, the periodic cyclic homology and the
corresponding Chern-Connes character.
