In a projector for projecting a multi-colored image, a control unit actuates each color channel with reference to fed-in image data such that one of the color subframes of the multi-colored image to be projected is generated. A projection optical system images the generated color subframes onto a projection surface such that the color subframes can be perceived as the multi-colored image to be projected. Each color channel is formed for the generation of a color subframe of a predetermined base color. The color location of the predetermined base color varies with the lightness to be generated. The control unit controls each color channel such that, for at least one picture point in the multi-colored image, the color location shift of the predetermined target color location caused by the color channel or the color channels is compensated for while retaining the target lightness.