convolution-invariant subalgebra generated by $f\in L^(X)$

Question

In the article arxiv.org/pdf/1301.1884.pdf, the author has used the language convolution-invariant subalgebra generated by $f\in L^\infty(X)$ where $X$ is a measure space, $G$ is a lcsc group and $(X,G)$ is an ergodic measure-preserving system. More precisely, he says that $L^1(G)\times L^\infty(X)\to L^\infty(X),$ $(c,f)\to c*f$ where $c*f(x):=\int_G c(g)f(g^{-1}x)dx.$ Then, "consider convolution-invariant subalgebra generated by $f\in L^\infty(X)$". What does the author actually mean by this terminology?