The generalized Kähler geometry of N = (2, 2) WZW-models

N = (2, 2), d = 2 supersymmetric non-linear σ-models provide a physical realization of Hitchin’s and Gualtieri’s generalized Kähler geometry. A large subclass of such models are comprised by WZW-models on even-dimensional reductive group manifolds. In the present paper we analyze the complex structures, type changing, the superfield content and the affine isometries compatible with the extra supersymmetry. The results are illustrated by an exhaustive discussion of the N = (2, 2) WZW-models on S3 × S1 and S3 × S3 where various aspects of generalized Kähler and Calabi-Yau geometry are verified and clarified. The examples illustrate a slightly weaker definition for an N = (2, 2) superconformal generalized Kähler geometry compared to that for a generalized Calabi-Yau geometry.