  This is an English translation of Raymond Debremaeker's 1976 Dutch-language
dissertation "Cohomologie met waarden in een gekruiste groepenschoof op een
situs" (Katholieke Universiteit te Leuven). I thank the University librarians
for sending me a copy of this text and Professor Debremaeker for allowing me to
post this translation of his dissertation on this server. Work on this
translation was supported by Chile's Fondecyt through grants 1120003 and
1160004.
