Figured I might as well make a topic about this as, despite being out for over a year on DS, it's about to be released for iPhone and iPad.
It's the most recent game written by Shu Takumi (Ace Attorney series) though the similarities, aside from being a predominantly story driven game, end there. You control a mysterious red-suited guy named Sissel who dies at the very start of the game, only to return to the world as a ghost with no memory of what happened to him or who he really is.
The gameplay is difficult to explain but basically Sissel, when he finds a corpse, has the ability to go back in time four minutes before they died and try to save them. This is accomplished by you pulling typical 'ghost stuff' and influencing objects in the real world ie: making a desk lamp swing around. The general idea is to create chain reactions and manipulate the environment to change the outcome of the given situation.
You can transfer yourself between two planes of existence, one of which allows you to transport your soul between objects and one which allows you to influence them, time stops while you're on the transport plane so scenarios can sometimes take longer than four minutes.
Later in the game you can also transport between areas via phone lines and there's the occasional puzzle set across multiple areas which adds some more depth.
Also it has this guy in it.