  N=(2,2), d=2 supersymmetric non-linear sigma-models provide a physical
realization of Hitchin's and Gualtieri's generalized Kaehler 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 S3xS1 and S3xS3 where
various aspects of generalized Kaehler and Calabi-Yau geometry are verified and
clarified. The examples illustrate a slightly weaker definition for an N=(2,2)
superconformal generalized Kaehler geometry compared to that for a generalized
Calabi-Yau geometry.
