DK Conjecture for Some $K$-inequivalences from Grassmannians

The DK conjecture of Bondal-Orlov and Kawamata states that there should be an embedding of bounded derived categories for any $K$-inequivalence, which is proved to be true for the toroidal case. In this paper, we construct examples of non-toroidal $K$-inequivalences from Grassmannians inspired by Kuznetsov, Kanemitsu, Ueda, and Morimura, and we show that these $K$-inequivalences satisfy the DK conjecture.