Hermitian algebraic $K$-theory and the root system~$D$
Fundamentalʹnaâ i prikladnaâ matematika, Tome 20 (2015) no. 3, pp. 251-256.

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For the root system $D$, we construct an analog of the Wagoner complex used in his proof of the equivalence of $K^Q_*$ and $K^{BN}_*$ (linear) algebraic $K$-theories. We prove that the corresponding $K$-theory $KU^D_*$ for the even orthogonal group is naturally isomorphic to the $KU^{BN}_*$-theory constructed by Yu. P. Solovyov and A. I. Nemytov.
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Th. Yu. Popelensky. Hermitian algebraic $K$-theory and the root system~$D$. Fundamentalʹnaâ i prikladnaâ matematika, Tome 20 (2015) no. 3, pp. 251-256. http://geodesic.mathdoc.fr/item/FPM_2015_20_3_a11/

[1] Klein I. S., Mikhalëv A. V., “Unitarnaya gruppa Steinberga nad koltsom s involyutsiei”, Algebra i logika, 9:5 (1970), 510–519 | MR

[2] Nemytov A. I., Solovev Yu. P., “$BN$-pary i ermitova $K$-teoriya”, Algebra, Izd-vo Mosk. un-ta, M., 1982, 102–118 | MR

[3] Anderson D., Karoubi M., Wagoner J., “Relations between algebraic $K$-theories”, Algebraic $K$-theory. I, Lect. Notes Math., 341, Springer, Berlin, 1973, 73–81 | DOI | MR

[4] Wagoner J., “Buildings, stratifications, and higher $K$-theory”, Algebraic $K$-theory. I, Lect. Notes Math., 341, Springer, Berlin, 1973, 148–165 | DOI | MR

[5] Wagoner J., “Equivalence of algebraic $K$-theories”, J. Pure Appl. Algebra, 11 (1977), 245–269 | DOI | MR