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Given a C$^*$-dynamical system $(A, G, \alpha)$ one defines a homomorphism,called the Chern-Connes character, that take an element in $K_0(A) \oplusK_1(A)$, the K-theory groups of the C$^*$-algebra $A$, and maps it into$H_{\mathbb{R}}^*(G)$, the real deRham cohomology ring of $G$. We explictlycompute this homomorphism for the examples $(\overline{\Psi_{cl}^0(S^1)}, S^1,\alpha)$ and $(\overline{\Psi_{cl}^0(S^2)}, SO(3), \alpha)$, where$\overline{\Psi_{cl}^0(M)}$ denotes the C$^*$-algebra generated by theclassical pseudodifferential operators of zero order in the manifold $M$ and$\alpha$ the action of conjugation by the regular representation(translations).

O carater de Chern-Connes para C$^*$-sistemas dinamicos calculado em algumas algebras de operadores pseudodiferenciais