The Noncommutative Chern-Connes Character of the Locally Compact Quantum Normalizer of SU(1,1) in SL(2,C)

We observe that the von Neumann envelope of the quantum algebra of functions on the normalizer of thegroup $\text{SU}(1,1)\cong \text{SL}(2,\mathbb{R})$ in $\text{SL}(2,\mathbb{C})$ via deformation quantization contains the von Neumann algebraic quantum normalizer of $\text{SU}(1,1)$ 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.