  We rigorously define the Liouville action functional for finitely generated,
purely loxodromic quasi-Fuchsian group using homology and cohomology double
complexes naturally associated with the group action. We prove that the
classical action - the critical point of the Liouville action functional,
considered as a function on the quasi-Fuchsian deformation space, is an
antiderivative of a 1-form given by the difference of Fuchsian and
quasi-Fuchsian projective connections. This result can be considered as global
quasi-Fuchsian reciprocity which implies McMullen's quasi-Fuchsian reciprocity.
We prove that the classical action is a Kahler potential of the Weil-Petersson
metric. We also prove that Liouville action functional satisfies holography
principle, i.e., it is a regularized limit of the hyperbolic volume of a
3-manifold associated with a quasi-Fuchsian group. We generalize these results
to a large class of Kleinian groups including finitely generated, purely
loxodromic Schottky and quasi-Fuchsian groups and their free combinations.
