Equality of topological and analytical local cyclic indices

Let $M$ be a quasi-conformal closed manifold. Let $\mathcal{A}_{\mu}$ be the algebra of pseudo-differential operators on $M$, localized by the support of operators about the diagonal, and let $\mathcal{J}=\mathcal{L}^{(\frac{1}{n},\infty)}$. For $u\in\mathbb{GL}_{N}(\mathcal{A}_{\mu}/\mathcal{J})$, let $Top^{Ch}Index(u)$ and $An^{Ch}Index(u)$ denote the corresponding topological and analytical indices. Equality of topological and analytical local cyclic indices. One has

$$Top^{Ch}Index(u)=An^{Ch}Index(u).$$

This is proposed in the localized periodic cyclic homology setting for quasi-conformal closed manifolds. The source supplies no evidence that the equality has been proved or disproved.