Noncommutative Solitons on Orbifolds

In the noncommutative field theory of open strings in a B-field, D-branes arise as solitons described as projection operators or partial isometries in a $C^*$ algebra. We discuss how D-branes on orbifolds fit naturally into this algebraic framework, through the examples of $R^n/G$, $T^n=R^n/Z^n$, and $T^n/G$. We also propose a framework for formulating D-branes on asymmetric orbifolds.