### Sur la K-theorie multiplicative, by Max Karoubi

In this paper we introduce a new type of K-theory, called "multiplicative
K-theory" kn(A) for A a Frechet algebra, which is intermediary between
algebraic K-theory, denoted Kn(A), and topological K-theory, denoted
Kntop(A). This new theory is computable in terms of Kntop(A) and cyclic
homology HC*(A). The homomorphism from Kn(A) to kn(A) we define in the
paper detects all known primary and secondary characterictic classes from
algebraic K-theory to cyclic homology (for example the Borel regulator if A
= the field of complex numbers). It is related to the multiplicative
character of a Fredholm module defined previously by A. Connes and the
author.

This paper has appeared in Proceedings of the Cyclic cohomology and
Noncommutative conference, Fields Institute Communications, Vol. 17,
American Mathematical Society (1997).

Max Karoubi <karoubi@math.jussieu.fr>