Thomas Schick: Real versus complex K-theory using Kasparov's bivariant KK-theory
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.
Thomas Schick