We introduce the notion of induced birational transformations of irreducible holomorphic symplectic sixfolds of the sporadic deformation type discovered by O'Grady. We give a criterion to determine when a manifold of OG 6 type is birational to K𝑣 (A, 𝜃), a moduli space of sheaves on an abelian surface. Then we determine when a birational transformation of K𝑣 (A, 𝜃) is induced by an automorphism of A. Referring to the Mongardi-Rapagnetta-Saccá birational model of manifolds of OG 6 type, we give a result to determine when a birational transformation is induced at the quotient. We give an application of these criteria in the non-symplectic case.

We prove that any symplectic automorphism of finite order on a manifold of type OG6 acts trivially on the Beauville-Bogomolov-Fujiki lattice and that any birational transformation of finite order acts trivially on its discriminant group. Moreover, we classify all possible invariant and coinvariant sublattices.

We classify nonsymplectic automorphisms of prime order on irreducible holomorphic symplectic manifolds of O'Grady's 6-dimensional deformation type. More precisely, we give a classification of the invariant and coinvariant sublattices of the second integral cohomology group.

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