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## Orbit closures of the Witt group actions

Proceedings of the Steklov Institute of Mathematics, Springer. 2019. Vol. 307. P. 193-197.

We prove that, for any prime integer $p\geqslant 2$, there exists an algebraic action of the two-dimensional Witt group $W_2(p)$ on an al\-geb\-raic variety $X$ and a point $x\in X$ such that the closure of the $W_2(p)$-orbit of $x$
in $X$ contains infinitely many $W_2(p)$-orbits.\;This is related to the problem of extending from characteristic zero to characteristic $p$ the classification of connected affine algebraic groups $G$ such that there are only finitely many $G$-orbits in every algebraic $G$-variety containing a dense open $G$-orbit.