sum of line bundles

Question

Let $f:X\times_k K\rightarrow X$ be the projection for a finite field extension and $X$ lets say a projective (or proper) scheme over $k$. Is it right that one has for a line bundle $L$ on $X\times_k K$: $f^*f_*L\simeq L^{\oplus d}$, where $d$ is the degree of the extension?