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This is now fixed:

sage: h.roots(ring=G)
[(a*b^2 + (a + 1)*b + a + 1, 1),
 (b^3 + b^2 + b + a, 1),
 (a*b^3 + a*b^2 + (a + 1)*b + 1, 1),
 ((a + 1)*b^3 + b^2 + b + 1, 1)]

This is now fixed:

sage: h.roots(ring=G)
[(a*b^2 + (a + 1)*b + a + 1, 1),
 (b^3 + b^2 + b + a, 1),
 (a*b^3 + a*b^2 + (a + 1)*b + 1, 1),
 ((a + 1)*b^3 + b^2 + b + 1, 1)]

Setting tags from confirmed_issue to fixed_issue.