  Let p be a rational prime and let F be a number field. Then, for each i>0,
there is a short exact localization sequence for K_{2i}(F). If p is odd or F is
nonexceptional, we find necessary and sufficient conditions for this exact
sequence to split: these conditions involve coinvariants of twisted p-parts of
the p-class groups of certain subfields of the fields F(\mu_{p^n}) for n\in N.
We also compare our conditions with the weaker condition WK^{et}_{2i}(F)=0 and
give some example.
