Extended BRST formulation of a non-commutative U(1) gauge model

In this short letter, we rediscuss the model for non-commutative U(1) gauge theory presented in [arXiv:0912.2634] and argue that by treating the "soft-breaking terms" of that model in the realm of an extended BRST symmetry, a future renormalization proof using Algebraic Renormalization should be possible despite the fact that the non-commutative model is non-local. In fact, the non-localities could be treated in a way similar to commutative gauge theories with axial gauge fixing where certain non-local poles appear.