Symmetries of the C⁎-algebra of a vector bundle

We consider C ⁎ -algebras constructed from compact group actions on complex vector bundles E → X endowed with a Hermitian metric. An action of G by isometries induces an the -correspondence Γ ( ) over consisting continuous sections, and associated Cuntz–Pimsner algebra O , so we can study crossed product ⋊ . If is free rank = n then prove that Morita–Rieffel equivalent to field Cuntz algebras orbit space / fiberwise, becomes products For transitive actions, show graph -algebra.