  In three preprints [Pan2],[Pan3] and the present one we prove
Grothendieck-Serre's conjecture concerning principal G-bundles over regular
semi-local domains R containing a finite field (here G is a reductive group
scheme). The present preprint contains main geometric presentation theorems
which are necessary for that. The preprint [Pan2] contains reduction of the
Grothendieck-Serre's conjecture to the case of a simple simply-connected group
scheme. The preprint [Pan3] contains a proof of Grothendieck-Serre's conjecture
for regular semi-local domains R containing a finite field. One of the main
result of the present preprint is Theorem 1.1. The Grothendieck--Serre
conjecture for the case of regular semi-local domains containing an infinite
field is proven in joint work due to R.Fedorov and I.Panin (see [FP]). Thus the
conjecture holds for regular semi-local domains containing a field.
