The nilpotence conjecture for higher K-theory of monoid rings

Let $M$ be an arbitrary commutative, cancellative, torsion-free monoid without non-trivial units, let $R$ be a regular ring, and let $i>0$. For every sequence $\operatorname{\frak c}=(c_1,c_2,\dots)$ of natural numbers with $c_j\geq 2$, and every element $x\in K_i(R[M])$, the homothety operations induced by multiplication by $c_1\cdots c_j$ satisfy

$$(c_1\cdots c_j)_*(x)\in K_i(R)$$

for all sufficiently large $j$, depending on $x$. Nilpotence conjecture. Under these hypotheses, every element of positive-degree higher $K$-theory of $R[M]$ is eventually carried into $K_i(R)$ by every sequence of homotheties with factors at least $2$. The conjecture strengthens the previously established positive results for $i=1$, $i=2$, and for monoids whose associated cone is simplicial; it would provide a uniform higher $K$-theoretic analogue of homotopy invariance and the known degree-zero result for seminormal monoids.