Bring a large pot of salted water to a boil. Add the tortellini, and bring the water back to a boil. Boil for two minutes, then drain and run under cold water. Add the drained tortellini to a large bowl.
To the tortellini, add the artichoke hearts, cheese balls, olives, sun dried tomatoes and red onion. Toss lightly. Drizzle in the pesto sauce and toss again. Add more pesto, if needed- so that everything is lightly coated. Sprinkle on fresh basil, for garnish. Cover with plastic wrap and refrigerate until ready to serve.