Bring large pot of water to a boil. Peel, seed and dice tomatoes, saving juice. Set aside in medium bowl.
In medium saucepan, heat oil over medium heat. Add garlic and cook, stirring often, 30 seconds. Add tomatoes with reserved juice and simmer 10 minutes. Add red peppers, olives and capers, and simmer 15 minutes more. Add basil during last 5 minutes of cooking.
When water boils, add salt and pasta, stirring to prevent sticking. Cook until just tender, about 5 to 7 minutes. Drain well and transfer to shallow serving bowl.
Spoon tomato mixture over capellini and toss briefly. Garnish with thinly sliced basil and cheese. Serve hot.