  Let X be a space, intended as a possibly curved spacetime, and A a precosheaf
of C*-algebras on X. Motivated by algebraic quantum field theory, we study the
Kasparov and Theta-summable K-homology of A interpreting them in terms of the
holonomy equivariant K-homology of the associated C*-dynamical system. This
yields a characteristic class for K-homology cycles of A with values in the odd
cohomology of X, that we interpret as a generalized statistical dimension.
