The subject of this thesis concerns deformation quantization for operator algebras, with considerations of some aspects of K-theory and certain concepts from non-commutative geometry.
The thesis studies deformation quantization of C*-algebras, building on an established framework for deforming C*-algebras equipped with group actions. Using a more recent formulation involving C*-algebraic crossed products and duality, a new method is developed for deforming C*-algebras equipped with a coaction of a locally compact group. The deformation or twisting is done with respect to a Borel 2-cocycle on the group. A result on invariance of K-theory under deformation is established. For the special case of theta deformation, in which case the n-torus group is considered, also index theory is investigated using tools of noncommutative geometry, leading to a result on the invariance of cyclic cohomology groups under deformation. Lastly a local index formula is given for the theta deformation of a manifold.