We study the group of group-like elements of a weak Hopf algebra and derive
an analogue of Radford's formula for the fourth power of the antipode S, which
implies that the antipode has a finite order modulo a trivial automorphism. We
find a sufficient condition in terms of Tr(S^2) for a weak Hopf algebra to be
semisimple, discuss relation between semisimplicity and cosemisimplicity, and
apply our results to show that a dynamical twisting deformation of a semisimple
Hopf algebra is cosemisimple.
