  For a smooth manifold X of dimension <d we construct a homomorphism from the
algebraic K-theory group in degree d of the algebra of smooth functions on X to
the degree -d-1 topological K-theory of X with coefficients in C/Z. This map
generalizes the map used by Suslin in order to calculate the torsion subgroup
of algebraic K-theory of C (the case X=*). We state and partially prove a
conjecture which compares the composition of the map above with the evaluation
against the K-homology class of a Dirac operator on X on the one hand, and the
Connes-Karoubi multiplicative character of the associated d-summable Fredholm
module on the other.
