### Real versus complex K-theory using Kasparov's bivariant KK-theory, by Thomas Schick

In this paper, we use the KK-theory of Kasparov to prove exactness of
sequences relating the K-theory of a real C*-algebra and of its
complexification (slightly generalizing results of Boersema).

We use this to relate the real version of the Baum-Connes conjecture
for a discrete group to its complex counterpart. In particular, the
complex Baum-Connes assembly map is an isomorphism if and only if the
real one is, thus reproving a result of Baum and Karoubi. After
inverting 2, the same is true for the injectivity or surjectivity part
alone.

A shorter (but less self contained) version, relying on the work of
Boersema, can be found at
http://www.uni-math.gwdg.de/schick/publ/real_complex_K.html

-- (Goettingen)

Thomas Schick <schick@uni-math.gwdg.de>