Bring a large pot of water to a boil, add pasta and cook according to the directions on the package.
While the pasta is cooking, heat the oil in a large skillet over a medium flame. Add the garlic and saute until fragrant, about 1 minute. Add the parsley, olives, capers, anchovy paste, oregano and crushed red pepper to the skillet, and saute for 2 minutes more. Add the tomatoes and simmer for about 5 minutes. Stir in the arugula and simmer for 1 minute more, until the greens wilt slightly.
When the pasta is done, drain it and add it to the skillet, tossing it with the sauce to combine. Top with grated cheese.
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