  We prove that two derived equivalent twisted K3 surfaces have isomorphic
periods. The converse is shown for K3 surfaces with large Picard number. It is
also shown that all possible twisted derived equivalences between arbitrary
twisted K3 surfaces form a subgroup of the group of all orthogonal
transformations of the cohomology of a K3 surface.
  The passage from twisted derived equivalences to an action on the cohomology
is made possible by twisted Chern characters that will be introduced for
arbitrary smooth projective varieties.
