Discard the outer cabbage leaves and cut in half. Core and, beginning at the core end, thinly slice. Place the cabbage in a large mixing bowl. Toss with 2 tablespoons salt and add cold water to cover. Let stand for 1 hour, drain and dry thoroughly.

In a large bowl, combine the mayonnaise with the vinegar and sugar. Add the cabbage and red pepper and toss with the mayonnaise dressing. Season to taste with salt and pepper. Refrigerate and remove 20 minutes before serving, adjust the seasoning.