  In the present paper we investigate a new class of infinite-dimensional
modules over the hyperalgebra of a semi-simple algebraic group in positive
chararacteristic called quasi-Verma modules. We provide a purely algebraic
construction of the global Grothendieck-Cousin complex corresponding to the
standard line bumdle ${\mathcal L}(\lambda)$ on the Flag variety of the
algebraic group stratified by Schubert cells. We prove that the complex
consists of direct sums of quasi-Verma modules for the highest weights of the
form $w\cdot\lambda$ for various elements $w$ of the Weyl group.
