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be the elements defined as follows: v +1 is the induced bundle of the canonical complex line bundle over the real projective space RP(l) by the natural projection D(m,l;ή)->SιIZ2=RP(l). α + v + 2 is the associated complex 2-plane bundle of the principal J7(2)-bundle induced from the principal DΠ-bundle S 2 m + 1 x5'-> D(m, l n) by the natural inclusion Dnc0(2)c 1/(2). γ is the image of σ®g ι by the induced homomorphism of the projection

On the $K$-ring of the orbit manifold $(S\sp{2m+1}\times S\spl)/D\sbn$ by the dihedral group $D\sbn$