1. Preheat oven to 350°. Line a baking sheet with parchment paper, and set aside.
2. Combine flour, oats, brown sugar, baking powder, baking soda, and salt in a food processor. Process 10 seconds or until oats are finely chopped. Add margarine; process until mixture resembles coarse meal.
3. Transfer mixture to a large mixing bowl; stir in cherries and ginger.
4. Combine buttermilk and egg whites in a small bowl; stir with a whisk. Add buttermilk mixture to dry mixture; stir just until a sticky dough forms.
5. Transfer dough to parchment paper-lined baking sheet, and pat into a 9-inch circle (about 1 inch thick). Sprinkle with all-purpose flour, if necessary, to keep dough from sticking to hands.
6. Divide dough by hand or with a knife into 8 equal wedges. Separate wedges slightly, and bake at 350° for 25 minutes or until browned and a wooden pick inserted in center comes out clean.