Wash and remove the outer leaves of the cabbage. Cut the cabbage into eighths and remove the core. Set aside.
Peel the onion and cut into eighths. Using a food processor fitted with the steel blade attachment, process the cabbage and onion, in manageable batches, until chopped finely. Scrape into a large container with a tight fitting lid. Set aside.
In a 1 quart or larger saucepan, combine the vinegar, sugar, V08, salt and celery seed. Bring to a boil and stir until the sugar is melted.
Pour the hot vinegar mixture over the cabbage and toss to coat well. Cover and refrigerate until completely chilled, at least 4 hours.