Cohomology of \(\mathcal{A}_\theta^{\mathrm{alg}}\rtimes\mathbb{Z}_2\) and its Chern-Connes pairing (Q1676071)

In the paper under review, the author calculates Hochschild and cyclic cohomology of \(\mathcal{A}_{\theta}^{\mathrm{alg}} \rtimes \mathbb{Z}_{2}\). The author also calculates the Chern-Connes pairing of \(6\) generators of \(HP^{\mathrm{even}}(\mathcal{A}_{\theta}^{\mathrm{alg}} \rtimes \mathbb{Z}_{2})\) with \(5\) generators of \(K_{0}(\mathcal{A}_{\theta}^{\mathrm{alg}} \rtimes \mathbb{Z}_{2})\), respectively. In the last of the paper, the author conjectures that those \(5\) generators span the group \(K_{0}(\mathcal{A}_{\theta}^{\mathrm{alg}} \rtimes \mathbb{Z}_{2})\).