Witt vectors with coefficients and characteristic polynomials over non-commutative rings

For a not-necessarily commutative ring R we define an abelian group W (R; M) of Witt vectors with coefficients in an R-bimodule M. These groups generalize the usual big Witt vectors of commutative rings and we prove that they have analogous formal properties and structure. One main result is that W(R) := W(R; R) is Morita invariant in R. For an R-linear endomorphism f of a finitely generated projective R-module we define a characteristic element chi(f) is an element of W(R). This element is a non-commutative analogue of the classical characteristic polynomial and we show that it has similar properties. The assignment f bar right arrow chi(f) induces an isomorphism between a suitable completion of cyclic K-theory K-0(cyc)(R) and W(R).