A construction of Gorenstein projective $\tau $-tilting modules

We give a construction of Gorenstein projective $\tau $-tilting modules in terms of tensor products of modules. As a consequence, we give a class of non-self-injective algebras admitting non-trivial Gorenstein projective $\tau $-tilting modules. Moreover, we show that a finite-dimensional algebra $\Lambda $ over an algebraically closed field is CM-$\tau $-tilting finite if $T_n(\Lambda )$ is CM-$\tau $-tilting finite, which gives a partial answer to a question on CM-$\tau $-tilting finite algebras posed by Xie and Zhang.