Noncommutative geometry in string and twisted Hopf algebra of diffeomorphism

We discuss the Hopf algebra structure in string theory and present the twist quantization as a unified formulation of the world sheet quantization of the string and the symmetry of the target spacetime. Applying it to the case with a nonzero B-field background, we explain a method to decompose the twist into two successive twists. There are two different possibilities of decomposition: The first is a natural decomposition from the viewpoint of the twist quantization, leading to a new type of twisted Poincaré symmetry. The second decomposition reveals the relation of our formulation to the twisted Poincaré symmetry on the Moyal type noncommutative space.