In this talk, we shall consider equivariant subproduct system of Hilbert spaces and their Toeplitz and Cuntz–Pimsner algebras. We will provide results about their topological invariants through K(K)-theory. More specifically, we will show that the Toeplitz algebra of the subproduct system of an SU(2)-representation is equivariantly KKequivalent to the algebra of complex numbers so that the (K)K- theory groups of the Cuntz–Pimsner algebra can be effectively computed using a Gysin exact sequence involving an analogue of the Euler class of a sphere bundle. Finally, we will discuss why and how C*-algebras in this class satisfy KK-theoretic Poincaré duality.[-]