Endomorphisms of semigroups of invertible nonnegative matrices over ordered rings

Let $R$ be a linearly ordered commutative ring with $1/2$ and $G_n(R)$ be the subsemigroup of $\mathrm{GL}_n(R)$ consisting of matrices with nonnegative elements. In the paper, we describe endomorphisms of this semigroup for $n\geq3$.