Star Piece
The 
Star Pieces are Quest items, for summon The legendary Pokémon Jirachi, at the Ancient Cave
You must obtain 5 Star Pieces to summon it.
They CAN be traded, and can be found while rumbling.
Item Description
A rare piece of a comet that once came from outer space.
The only available action for this item is to give it to a Pokémon.