Cut the cabbage into wedges. Cut out and discard the hard core from each wedge. Using a food processor fitted with the slicing disk, cut the cabbage into fine shreds. (The cabbage can also be thinly sliced by hand). Transfer to a large bowl.
Fit the processor with a shredding disk and shred the carrots. (The carrots can also be shredded by hand using the largest holes of a box grater-shredder). Add the carrots to the bowl with the cabbage.
Sprinkle the cabbage and carrots with the vinegar and mix well. Stir in the bell pepper strips and green onion.
Add the mayonnaise and Old Bay Seasoning and mix well. Cover and refrigerate until chilled, at least 2 hours. Serve cold.