Preheat oven to 450 degrees F. Cut each grapefruit in half horizontally; cut a very thin slice from the bottom of each half so grapefruits will sit flat. Using a grapefruit knife or other small knife, cut around the outer edge to loosen fruit from shell. Cut between each segment and membrane to loosen it.
In a medium bowl, combine orange sections, banana, cherries, and orange liqueur. Place grapefruit halves, cut sides up, in a 3-quart rectangular baking dish. Mound the orange mixture on top of grapefruit halves. Drizzle with oil. In a small bowl, combine brown sugar and cinnamon; sprinkle over orange mixture.
Bake about 12 minutes or until grapefruits are warm and topping is heated through.