  Models of gravity with variable G and Lambda have acquired greater relevance
after the recent evidence in favour of the Einstein theory being
nonperturbatively renormalizable in the Weinberg sense. The present paper
applies the Arnowitt-Deser-Misner (ADM) formalism to such a class of
gravitational models. Are modified action functional is then built which
reduces to the Einstein-Hilbert action when G is constant, and leads to a
power-law growth of the scale factor for pure gravity and for a massless Phi**4
theory in a Universe with Robertson-Walker symmetry, in agreement with the
recently developed fixed-point cosmology. Interestingly, the
renormalization-group flow at the fixed point is found to be compatible with a
Lagrangian description of the running quantities G and Lambda.
