Twist symmetry and gauge invariance

By applying properly the concept of twist symmetry to the gauge invariant theories, we arrive at the conclusion that the previously proposed in the literature noncommutative gauge theories, with the use of ⋆-product, are the correct ones, which possess the twisted Poincaré symmetry. At the same time, a recent approach to twisted gauge transformations is in contradiction with the very concept of gauge fields arising as a consequence of local internal symmetry. Detailed explanations of this fact as well as the origin of the discrepancy between the two approaches are presented.