### A descent theorem in topological K-theory, by Max Karoubi

Jun 15, 2000: An improved version of the paper with a better spectral
sequence has been posted.

Let A be a Banach algebra and A' its complexification. In this paper we show
that the homotopy fixed point set of K(A'), the topological K-theory space of
A', under complex conjugation is just K(A), the topological K-theory space of
A. This result generalizes the well known fact that BO is BU^hZ/2. The
proof uses in an essential way Atiyah's KR theory and the Clifford algebra
definition of higher K-groups.

Max Karoubi <karoubi@math.jussieu.fr>