A quantum covering group is an algebra with parameters q and π subject to π 2 = 1 and it admits an integral form; it specializes to the usual quantum group at π = 1 and to a quantum supergroup of anisotropic type at π = −1. In this paper we establish the Frobenius-Lusztig homomorphism and Lusztig-Steinberg tensor product theorem in the setting of quantum covering groups at roots of 1. The specialization of these constructions at π = 1 recovers Lusztig's constructions for quantum groups at roots of 1.2010 Mathematics Subject Classification. Primary 17B37.

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