<p>We say that a group <i>G</i> is weakly surjunctive (resp. linearly surjunctive) if for every finite group <i>V</i> (resp. every finite vector space <i>V</i>), all injective <i>G</i>-equivariant uniformly continuous self-maps <i>V</i>^<i>G</i> ↺ which are also group (resp. linear) homomorphisms must be surjective. Examples of such groups include all sofic groups and more generally all surjunctive groups, i.e., groups which satisfy Gottschalk’s surjunctivity conjecture. We establish reversibility and invertibility results for injective endomorphisms of symbolic group varieties over weakly surjunctive group universes with algebraic group alphabets. As an application, we show that the group ring <i>R</i>[<i>G</i>] is stably finite whenever <i>G</i> is a weakly surjunctive group and <i>R</i> is the endomorphism ring of a commutative algebraic group over an algebraically closed field.</p>