2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/166409Given a C$^*$-dynamical system $(A, G, α)$ one defines a homomorphism, called the Chern-Connes character, that take an element in $K_0(A) \oplus K_1(A)$, 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 explictly compute this homomorphism for the examples $(\overline{Ψ_{cl}^0(S^1)}, S^1, α)$ and $(\overline{Ψ_{cl}^0(S^2)}, SO(3), α)$, where $\overline{Ψ_{cl}^0(M)}$ denotes the C$^*$-algebra generated by the classical pseudodifferential operators of zero order in the manifold $M$ and $α$ the action of conjugation by the regular representation (translations).This is a PhD thesis in portuguese supervised by Severino T. MeloOperator AlgebrasK-Theory and Homologytext