Equivariant maps between real linear representations of finitely generated groups

Question

Let $G$ be a finitely generated group, ad let $(V,\rho)$ and $(W,\phi)$ be two finite dimensional linear representations of $G$ over $\mathbb{R}$. Given a linear map $f:V\to W$ it's immediate to check whether $f$ is equivariant or not, but I find it hard to find an equivariant map if I'm not given one.

Is there any results that classify or characterize all the equivariant linear maps between the two?

Answer 1

Just take an arbitrary linear map and average it over $G$.