## Hyperbolicity of orthogonal involutions

### Summary

We show that a non-hyperbolic orthogonal involution on a central simple algebra over a field of characteristic $\ne 2$ remains non-hyperbolic over some splitting field of the algebra.

### Mathematics Subject Classification

14C15, 16K20, 14C25

### Keywords/Phrases

algebraic groups, involutions, projective homogeneous varieties, Chow groups and motives, Steenrod operations