### Rigidity for Orientable Functors, by Ivan A. Panin and Serge A. Yagunov

In this paper we introduce the notion of orientable cohomology theory on the
category of projective smooth schemes, define a family of transfer maps and,
as a consequence of these constructions, prove that taken with finite
coefficients such cohomology doesn't change after an extension of
algebraically closed fields.

This result generalizes the old and remarkable Suslin's theorem about
K-theory of algebraically closed fields. Besides K-theory, we treat the
following examples of orientable theories: Etale Cohomology, Motivic
Cohomology, Algebraic Cobordism.

This paper is a refined version of our
Max Plank Institute preprint #69, 2000.

Ivan A. Panin <panin@pdmi.ras.ru>

Serge A. Yagunov <serge.yagunov@uni-essen.de>