Using the large grater wheel of a food processor, grate together the cabbage, carrots, onion, and green pepper. Transferring these vegetables to a large bowl, mix them together well. In a separate bowl, whisk together mayonnaise, vinegar, sugar, salt, and pepper. Pour mayonnaise mixture onto vegetables. Blend well. Allow about 1 hour for this mixture to sit in the refrigerator so it gets cold and the tastes blend together.