The printing process doesn't use light to express color, it uses ink, which absorbs light. Cyan absorbs all colors except cyan, yellow absorbs all colors except yellow, and so on. This is why when all the inks are added together in equal parts, all light is absorbed, giving black.
Each channel of the RGB color space is governed by it's complimentary color in the CYMK color space. Adding or removing the complimentary color provides the variations. Here is a short list of who controls whom in the RGB-CYMK relationship
Red is controlled by Cyan
Green is controlled by Magenta
Blue is controlled by Yellow
The CYM filters on enlargers used in color film photography for printing use this system to control the overall tint of an image and get the colors to separate. The "K" in color film printing is the length of time one exposes the paper, controlling density and detail.
The digital darkroom continues the tradition. The "K" for black ink, which is used because the maximum of CYM alone doesn't produce a "true" black, but rather a very, very dark gray usually lacking detail. The black ink is the final touch which adds detail and contrast.
To see the relationship of RGB and CYMK in Photoshop, open up the "Color Balance..." adjustment layer. There you will see the digital version of the traditional film enlarger. Moving the slider for each will adjust the overall tint of the image, just like in color film photography