We show theoretically that the strong interaction of a two-dimensional electron gas (2DEG) with a dressing electromagnetic field drastically changes its transport properties. Particularly, the dressing field leads to the giant increase of conductivity (which can reach thousands of percents), results in nontrivial oscillating dependence of conductivity on the field intensity, and suppresses the weak localization of 2DEG. As a consequence, the developed theory opens an unexplored way to control transport properties of 2DEG by a strong high-frequency electromagnetic field. From experimental viewpoint, this theory is applicable directly to quantum wells exposed to a lasergenerated electromagnetic wave.