Store the whole head of cabbage in a plastic bag in the refrigerator for up to a week, two weeks if it is fresh from the garden. But remember, the older it gets, the stronger the flavor and odor will be. 

Cabbage will lose freshness rapidly once the head is chopped, so plan on using it within a day. If you only need half a head, place the remaining half in a plastic bag and shake a few drops of water onto the cut side. Close the bag and refrigerate. The cut half should last another few days if it was fairly fresh when you cut it.