In a pot of boiling salted water, cook the tortellini for 5 minutes.
Set aside to cool after draining.
Combine the tortellini, marinated artichoke hearts, roasted red pepper, kalamata olives, halved cherry tomatoes, and garlic in a large bowl.
Combine the mayonnaise, pesto, parmesan cheese, olive oil, and vinegar in another bowl.
Toss the tortellini salad with the dressing.
Then refrigerate for one hour.