  Every Fourier--Mukai equivalence between the derived categories of two K3
surfaces induces a Hodge isometry of their cohomologies viewed as Hodge
structures of weight two endowed with the Mukai pairing. We prove that this
Hodge isometry preserves the natural orientation of the four positive
directions. This leads to a complete description of the action of the group of
all autoequivalences on cohomology very much like the classical Torelli theorem
for K3 surfaces determining all Hodge isometries that are induced by
automorphisms.
