In studying automorphisms of algebraic varieties it is natural to consider the induced action on the cohomology ring, say, with complex coefficients. In many cases the induced action is faithful, which can be understood as certain rigidity of the automorphisms. Yet there do exist algebraic varieties that have nontrivial automorphisms acting on the cohomology ring. Such automorphisms are called numerically trivial. In this talk I will report on a characterization of algebraic surfaces of general type having a maximal possible group of numerically trivial automorphisms. This is partly based on joint work with Jin-Xing Cai and Lei Zhang.

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