In a bowl stir together beet, turnip, carrot, onion, and cabbage. In a small bowl combine oil, lemon juice, sugar, 1 teaspoon salt, and 1/2 teaspoon pepper. Add to beet mixture; toss to coat. Cover; chill overnight.
Let mixture stand at room temperature for 30 minutes before serving. Arrange greens on 6 salad plates. Using a slotted spoon, top greens with beet mixture. Sprinkle with cherries and seeds. Makes 6 servings.