Sprinkle pork evenly with salt and pepper. Place in a baking dish or large zip-top plastic freezer bag.
Stir together yogurt and next 6 ingredients. Reserve 1 cup yogurt mixture; cover and chill.
Spoon remaining yogurt mixture over pork, rubbing evenly over pork. Cover or seal, and chill 2 hours. Remove pork from marinade, discarding marinade.
Grill, covered with grill lid, over medium-high heat (350° to 400°), 20 minutes, turning once, or until meat thermometer inserted into thickest portion registers 155°. Remove from heat; let stand 10 minutes. Cut into 1/2-inch slices; serve with reserved 1 cup yogurt mixture.