Noncommutative Symmetries and Gravity
  Spacetime geometry is twisted (deformed) into noncommutative spacetime geometry, where functions and tensors are now star-multiplied. Consistently, spacetime diffeomorhisms are twisted into noncommutative diffeomorphisms. Their deformed Lie algebra structure and that of infinitesimal Poincare' transformations is defined and explicitly constructed.   This allows to construct a noncommutative theory of gravity. 
Paolo Aschieri