On $R$-equivalence of Automorphism Groups of Associative Algebras

Let $A$ be a finite-dimensional associative $k$-algebra with identity. The primary aim of this paper is to study the rationality properties of the group of all $k$-algebra automorphisms of $A$, as an affine algebraic group over an arbitrary field $k$. We investigate mainly the $R$-equivalence property of the identity component of ${\mathrm{A}\mathrm{u}\mathrm{t}}_k(A)$ over a perfect field $k$.