Gysin sequences and SU(2)-symmetries of C∗-algebras

Motivated by the study of symmetries of (Formula presented.) -algebras, as well as by multivariate operator theory, we introduce the notion of an (Formula presented.) -equivariant subproduct system of Hilbert spaces. We analyse the resulting Toeplitz and Cuntz–Pimsner algebras and provide results about their topological invariants through Kasparov's bivariant (Formula presented.) -theory. In particular, starting from an irreducible representation of (Formula presented.), we show that the corresponding Toeplitz algebra is equivariantly (Formula presented.) -equivalent to the algebra of complex numbers. In this way, we obtain a six-term exact sequence of (Formula presented.) -groups containing a noncommutative analogue of the Euler class.