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Renormalization group techniques are used in order to obtain the improvednon-local gravitational effective action corresponding to any asymptoticallyfree GUT, up to invariants which are quadratic on the curvature. Thecorresponding non-local gravitational equations are written down, both for thecase of asymptotically free GUTs and also for quantum R$^2$-gravity. Theimplications of the results when obtaining the flux of vacuum radiation throughthe future null infinity are briefly discussed.Comment: LaTeX file, 11 pages, no figure

A RENORMALIZATION GROUP IMPROVED NONLOCAL GRAVITATIONAL EFFECTIVE LAGRANGIAN