| Summary: | The cohomogeneity of a transformation group ([italic capitals]G, X) is, by definition, the dimension of its orbit space, [italic]c = dim [italic capitals]X, G. We are concerned with the classification of differentiable compact connected Lie transformation groups on (homology) spheres, with [italic]c [less than or equal to symbol] 2, and the main results are summarized in five theorems, A, B, C, D, and E in part I. This paper is part II of the project, and addresses theorems D and E.D examines the orthogonal model from theorem A and orbit structures, while theorem E addresses the existence of "exotic" [italic capital]G-spheres
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