Shihou Sekai no Ou

In the year 1800 B.C. there was an ancient city called Babilim, a very important trade center, and this is where a teenage boy named Namuru lives and attends school. Namuru is instantly attracted to the mysterious new girl in school, Shaz, and she later gets them in trouble with some street thugs when she steals from a merchant. However, Shaz removes the head of the attacker without killing him and scares the thugs away. She explains to the confused Namuru that she possesses 1/50th blood of Marduke, the city of Babilim's God of War, and that he does as well. With the blood of a god within him, she explains that they can tap into a small part of the almighty power to manipulate dimensions which in turn allows them to remove and transport objects (explaining the "beheading" of the street thug). What's even more shocking is that Shaz wants Namuru to help her take over Babilim in order to destroy the kingdom! (Source: MangaHelpers)