The Burnside ring $B(G)$ of a finite group $G$ is the ring of all finite $G$-sets under disjoint union and Cartesian product. It is well known that $\mathbb{Q} \otimes B(G)$ has as basis $\{[G/H] \mid H \le_G G \}$ ($\le_G$ means $H$ is taken up to $G$-conjugacy) and there is a natural surjection $\theta$ onto the representation ring $\mathbb{Q} \otimes R(G)$ which has basis the images of $\{[G/H] \mid H \le_G G, \mbox{ $H$ cyclic } \}$. The kernel $ker(\theta)$ is called the set $K(G)$ of Brauer relations. For example, if $G=S_3$, $K(G)$ is generated by a single relation $$[G/\langle () \rangle]-2[G/\langle (1,2) \rangle]-[G/\langle (1,2,3) \rangle]+2[G/G].$$
Observe that applying the augmentation map $\epsilon: [G/H] \mapsto 1$ to this relation gives $1-2-1+2=0$. More generally I have checked that all relations of all groups $G$ with $|G| \le 63$ vanish under $\epsilon$. Is this true in general?