Whisk 1 cup yogurt, 1/4 cup juice, the ginger, curry, 3/4 teaspoon cumin, the cayenne, and turmeric together in a bowl; salt and pepper to taste for marinade.

Rinse and pat chicken dry. Place in a large resoluble plastic bag and pour marinade over chicken. Seal bag, then turn until chicken is evenly coated. Place bag in a bowl, to catch any leaks, and marinate, chilled, for at least 6 hours or overnight.

Preheat grill. Place potatoes in a 5-quart pot. Cover with salted cold water by 2 inches and simmer until fork tender, about 15 minutes depending on size of potatoes. Drain in a colander and rinse with cold water until cool enough to handle but still warm.

Whisk remaining 1/4 cup yogurt, 2 tablespoons juice, and 1/2 teaspoon cumin together in a large bowl; salt and pepper to taste. Heat a small skillet over moderate heat until hot and toast mustard seeds, shaking skillet, until fragrant, about 30 seconds. Immediately whisk seeds into yogurt mixture. Halve potatoes and add to bowl, gently tossing to combine. Transfer potato salad to a serving bowl and top with cilantro and onion.

Remove chicken from marinade and discard marinade. Grill, covered, on a lightly oiled rack over moderate heat, turning and adjusting heat to avoid burning chicken, 20 minutes. Uncover and continue to grill until chicken is cooked through, about 10 more minutes.

Serve chicken with potatoes and lime wedges on the side. Makes 4 servings.