  We prove that the group of area-preserving diffeomorphisms of the 2-sphere
admits a non-trivial homogeneous quasimorphism to the real numbers with the
following property. Its value on any diffeomorphism supported in a sufficiently
small open subset of the sphere equals to the Calabi invariant of the
diffeomorphism. This result extends to more general symplectic manifolds: If
the symplectic manifold is monotone and its quantum homology algebra is
semi-simple we construct a similar quasimorphism on the universal cover of the
group of Hamiltonian diffeomorphisms.
