Combine first 3 ingredients in a saucepan. Bring to a boil over medium-high heat. Reduce heat, and simmer, uncovered, for 5 minutes. Discard cinnamon stick. Chill grapefruit mixture in refrigerator.
Fill 4 (8-ounce) glasses with ice; add 1/3 cup grapefruit mixture to each. Fill glasses with ginger ale; stir gently. Garnish, if desired.
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