Geodesic
Thom isomorphism in the “twice” equivariant $K$-theory of $C^*$-fibrations
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part V, Tome 266 (2000), pp. 245-253 Cet article a éte moissonné depuis la source Math-Net.Ru

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A theorem on the Thom isomorphism for the $K$-theory of fibrations whose fiber is a projective module over a $C^*$-algebra is proved in the situation where a compact Lie group acts on the algebra and on the total space as well. 
@article{ZNSL_2000_266_a14,
     author = {E. V. Troitskii},
     title = {Thom isomorphism in the {\textquotedblleft}twice{\textquotedblright} equivariant $K$-theory of $C^*$-fibrations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {245--253},
     year = {2000},
     volume = {266},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_266_a14/}
}
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E. V. Troitskii. Thom isomorphism in the “twice” equivariant $K$-theory of $C^*$-fibrations. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part V, Tome 266 (2000), pp. 245-253. http://geodesic.mathdoc.fr/item/ZNSL_2000_266_a14/