Geodesic
Rationality Problem for Classifying Spaces of Spinor Groups
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebra, number theory, and algebraic geometry, Tome 307 (2019), pp. 132-141

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We study stable rationality and retract rationality properties of the classifying spaces of split spinor groups $\mathbf {Spin}_n$ over a field $F$ of characteristic different from $2$. 
@article{TM_2019_307_a5,
     author = {Alexander S. Merkurjev},
     title = {Rationality {Problem} for {Classifying} {Spaces} of {Spinor} {Groups}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {132--141},
     publisher = {mathdoc},
     volume = {307},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2019_307_a5/}
}
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Alexander S. Merkurjev. Rationality Problem for Classifying Spaces of Spinor Groups. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebra, number theory, and algebraic geometry, Tome 307 (2019), pp. 132-141. http://geodesic.mathdoc.fr/item/TM_2019_307_a5/