Noncommutative gerbes and deformation quantization
  We define noncommutative gerbes using the language of star products. Quantized twisted Poisson structures are discussed as an explicit realization in the sense of deformation quantization. Our motivation is the noncommutative description of D-branes in the presence of topologically non-trivial background fields. 
Paolo Aschieri, Igor Bakovic, Branislav Jurco, Peter Schupp