Geodesic
$K$-groups of quadratic extensions of rings
Matematičeskie zametki, Tome 58 (1995) no. 2, pp. 272-280

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We construct the Levin braid connecting the Tate cohomology of $K$-groups for quadratic extensions of rings with antistructures. Explicit formulas for isomorphisms of relative cohomology groups for the induced mapping and for the transfer mapping are obtained; these formulas are necessary in the construction of the Levin braid. 
@article{MZM_1995_58_2_a8,
     author = {Yu. V. Muranov},
     title = {$K$-groups of quadratic extensions of rings},
     journal = {Matemati\v{c}eskie zametki},
     pages = {272--280},
     publisher = {mathdoc},
     volume = {58},
     number = {2},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1995_58_2_a8/}
}
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Yu. V. Muranov. $K$-groups of quadratic extensions of rings. Matematičeskie zametki, Tome 58 (1995) no. 2, pp. 272-280. http://geodesic.mathdoc.fr/item/MZM_1995_58_2_a8/