Cut cabbage in half. Shred very fine on a slicer, or by hand.
Put sugar, vinegar, oil, salt, and pepper into a non-metal bowl. Stir to dissolve sugar. Add cabbage. Toss, cover, refrigerate, and let marinate for at least 8 hours. Overnight if you wish. Toss occasionally.
Put into a bowl and serve as is done in Picardy, or spoon it into dark green Bibb lettuce leaves and serve as individual salads.