Geodesic
Chow ring of generic maximal orthogonal Grassmannians
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 29, Tome 443 (2016), pp. 147-150

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We compute the Chow ring of the maximal orthogonal Grassmannian corresponding to a versal torsor, and in particular show that it has no torsion as an abelian group. 
@article{ZNSL_2016_443_a11,
     author = {V. A. Petrov},
     title = {Chow ring of generic maximal orthogonal {Grassmannians}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {147--150},
     publisher = {mathdoc},
     volume = {443},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_443_a11/}
}
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V. A. Petrov. Chow ring of generic maximal orthogonal Grassmannians. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 29, Tome 443 (2016), pp. 147-150. http://geodesic.mathdoc.fr/item/ZNSL_2016_443_a11/