The Chern-Connes Character for pseudodifferential operators on the sphere

We compute the Chern-Connes character (a map from the $K$-theory of a C${}^{\ast }$-algebra under the action of a Lie group to the cohomology of its Lie algebra) for the $L^2$-norm closure of the algebra of all classical zero-order pseudodifferential operators on the sphere under the canonical action of ${\rm SO}(3)$\mathrm{.}Weshowthatitsimageis$$\mathbb{R}$$ if the trace is the integral of the principal symbol.