  Motivated by the study of symmetries of C*-algebras, as well as by
multivariate operator theory, we introduce the notion of an SU(2)-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 K-theory. In particular, starting from an
irreducible representation of SU(2), we show that the corresponding Toeplitz
algebra is equivariantly KK-equivalent to the algebra of complex numbers. In
this way, we obtain a six term exact sequence of K-groups containing a
noncommutative analogue of the Euler class.
