Season pork with salt and pepper. Grill pork, covered, indirectly (put coals around the edges of the meat rather than below it) over medium-high heat for 25 minutes. Meanwhile, mix preserves and soy sauce. Brush 2 tablespoons of it on pork. Cover and grill 5 to 10 minutes more, or until the pork is cooked through Remove from grill; brush 2 more tablespoons apricot mixture over pork. Cover with foil and let stand.
Brush apricots with oil and grill directly over medium heat for 2 minutes per side, or until slightly softened and browned.
Slice pork and serve with remaining apricot mixture and grilled apricots on the side.