Wash the cabbage under cold running water. Remove tough outer leaves, and cut the cabbage into quarters. To shred the cabbage, cut out the core and slice the quarters crosswise into 1/8 inch-wide strips.
Drop the cabbage into a large mixing bowl. Add the onion and bell pepper, and mix well with a spoon.
In a small bowl, combine the mayonnaise, beer, celery seed, salt and a few grindings of black pepper. Stir with a wire whisk until all the ingredients are blended. Pour the mixture over the cabbage and toss together gently but thoroughly. Taste for seasoning.
Cover the bowl with plastic wrap and refrigerate the coleslaw for about an hour before serving.