About symmetry of the gravitational action

The Einstein equations are investigated by imbedding of the metric tensor to the affinely connected space. It is shown that if using of the Einstein equations, then, despite the action functional invariance being violated with respect to the diffeomorphism group by the background object, a new infinite-parameter invariance appears, i.e., the action invariance can be extended from the group of motions of the background object to any infinite-parameter group. 10 refs