Flat space limit of the -deformation of the action

Can we view as the deformation of the flat space action?

Notice that is a parity-even deformation, while is parity-odd. One would think that these two deformations are independent of each other, and one could separate them and write:

— a valid deformation of the flat space action ?

If true, this would have implied that there exists such a deformation of the BRST structure , of the order , that:

In other words: