Looking at the definition of the Kunneth morphism in SGA4, XVII, 5.4.1.4, there is the notation $$Rf_*K \overset{\mathbb{L}}{\boxtimes}_{\mathcal{A}_0} Rg_* L \rightarrow Rh_*(K \overset{\mathbb{L}}{\boxtimes}_{\mathcal{A}_0} L).$$
Likewise, in this entry on the Kunneth formula in the Encyclopedia of Math, there is $$Rp_*(\mathcal{F})\overset{L}{\bigotimes_{\mathcal{O}_S}} Rq_*(\mathcal{G}) = Rh_*\left(\mathcal{F} \overset{L}{\bigotimes_{\mathcal{O}_S}} \mathcal{G}\right).$$
I can't seem to find a definition of this tensor, nor if $\mathbb{L}$ or $L$ is merely part of the symbol or an object in its own right.