Stapledon's trivial-representation conjecture for equivariant Ehrhart coefficients

Let $G$ be a finite group, let $M$ be a lattice, let $\rho:G\to\operatorname{Aff}(M)$ be an affine representation, and let $P$ be a $G$-invariant lattice polytope. Assume that $h^*(P,\rho;t)$ is a polynomial, and write $h^*(P,\rho;t)_m\in R(G)$ for the coefficient of $t^m$, where $m$ is any nonnegative integer. Stapledon's trivial-representation conjecture. If $h^*(P,\rho;t)_m$ is nonzero and effective, then the trivial representation occurs with nonzero multiplicity in $h^*(P,\rho;t)_m$. The conjecture was verified for the symmetric-group action on the permutahedron, but the paper gives a counterexample, so it is refuted.