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We establish a relation between time-like, light-like and space-like orbitsof the non-compact E{7(7)}(R)symmetry and discrete E{7(7)}(Z) invariants. Wediscuss the U-duality invariant formula for the degeneracy of states d(Q) whichin the approximation of large occupation numbers reproduces theBekenstein-Hawking entropy formula for regular black holes with AdS_2 horizon.We explain why the states belonging to light-like orbits, corresponding toclassical solutions of "light black holes with null singularity", decouple fromthe corresponding index. We also present a separate U-duality invariant formulafor the class of light-like orbits specified by discrete E{7(7)}(Z) invariants.We conclude that the present study of the non-perturbative sector of the theorydoes not reveal any contradiction with the conjectured all-loop perturbativefiniteness of D=4 N=8 supergravity.

Observations on Arithmetic Invariants and U-Duality Orbits in N =8 Supergravity