In a large bowl, dissolve yeast in warm water. Add the bread flour, oil, honey, salt and 4 cups of the whole wheat flour. Beat until smooth. Stir in the sunflower kernels and enough remaining flour to form a firm dough.
Turn onto a floured surface; knead until smooth and elastic, about 6-8 minutes. Place in a greased bowl, turning once to grease the top. Cover and let rise in a warm place until doubled, about 1 hour.
Punch dough down; divide into three portions. Shape into loaves; place in three greased 8x4 inch loaf pans. Cover and let rise until doubled, about 30 minutes.
Bake at 350 degrees for 35-40 minutes or until golden brown. Remove from pans to wire racks to cool.