Dadeʹs invariant conjecture for the Chevalley groups of type G2 in the defining characteristic

This paper is part of a program to study the conjecture of E.C. Dade on counting characters in blocks for several finite groups. In this paper, we verify Dadeʹs invariant conjecture for the Chevalley groups G2(pa) in the defining characteristic when p≠2 or 3. This implies Dadeʹs final conjecture when p≠2 or 3.