  An approach to the construction of index formulas for elliptic operators on
singular manifolds is suggested on the basis of K-theory of algebras and cyclic
cohomology. The equivalence of Toeplitz and pseudodifferential quantizations,
well known in the case of smooth closed manifolds, is extended to the case of
manifolds with conical singularities. We describe a general construction that
permits one, for a given Toeplitz quantization of a C^*-algebra, to obtain a
new equivalent Toeplitz quantization provided that a resolution of the
projection determining the original quantization is given.
