  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.
