Geodesic
On homotopization of the unitary $K_1$-functor
Algebra i analiz, Tome 20 (2008) no. 5, pp. 99-108.

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A unitary $K_1$-analog of the Karoubi–Villamayor functor is constructed, which solves the problem of homotopization of the unitary $K_1$-functor on the category of rings with involution.
Keywords: Ring with involution, unitary group, homotopization of a functor, Higman's trick, Karoubi–Villamayor functors, hyperbolic rings. 
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V. I. Kopeǐko. On homotopization of the unitary $K_1$-functor. Algebra i analiz, Tome 20 (2008) no. 5, pp. 99-108. http://geodesic.mathdoc.fr/item/AA_2008_20_5_a4/

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