  The Chern isomorphism determines the free part of the K-groups from ordinary
cohomology. Thus to really understand the implications of K-theory for physics
one must look at manifolds with K-torsion. Unfortunately there are not many
explicit examples, and usually for very symmetric spaces. Cartesian products of
RP^n are examples where the order of the torsion part differs between K-theory
and ordinary cohomology. The dimension of corresponding branes is also
discussed. An example for a Calabi-Yau manifold with K-torsion is given.
