Open N=2 strings in a B-field background and noncommutative self-dual Yang-Mills

In the presence of D-branes, fermionic N=2 strings in 2+2 dimensions can be coupled to a K"ahler NS-NS two-form B. We present the corresponding action which produces N=2 supersymmetric boundary conditions and discuss the Seiberg-Witten zero-slope limit. After recalling the constraints on the Chan-Paton gauge group, we demonstrate for U(n) groups that the open N=2 string with a nonzero B-field coincides on tree level with noncommutative self-dual Yang-Mills. Several misconceptions of hep-th/0011206 are corrected.