Hrushovski's pseudofinite fixed-point conjecture for generic automorphisms

Let $G$ be an infinite simple group of finite Morley rank, and let $\alpha$ be a generic automorphism of $G$. The group of fixed points of $\alpha$ is $\{g\in G:\alpha(g)=g\}$.

Hrushovski's fixed-point conjecture. The group of fixed points of $\alpha$ is pseudofinite, that is, an infinite model of the theory of finite groups.

The conjecture is implied by the Algebraicity Conjecture and concerns a proposed bridge between simple groups of finite Morley rank and pseudofinite groups. The source gives no resolution, so its status remains open.