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We discuss reality conditions and the relation between spacetimediffeomorphisms and gauge transformations in Ashtekar's complex formulation ofgeneral relativity. We produce a general theoretical framework for thestabilization algorithm for the reality conditions, which is different fromDirac's method of stabilization of constraints. We solve the problem of theprojectability of the diffeomorphism transformations fromconfiguration-velocity space to phase space, linking them to the realityconditions. We construct the complete set of canonical generators of the gaugegroup in the phase space which includes all the gauge variables. This resultproves that the canonical formalism has all the gauge structure of theLagrangian theory, including the time diffeomorphisms.Comment: Submitted to Phys. Rev. D15. - 17 page

Gauge group and reality conditions in Ashtekar’s complex formulation of canonical gravity