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In this article we prove some period relations for the ratio of Deligne'speriods for certain tensor product motives. These period relations give amotivic interpretation for certain algebraicity results for ratios ofsuccessive critical values for Rankin-Selberg L-functions for ${\rm GL}_n\times {\rm GL}_{n'}$ proved by G\"unter Harder and the second author.

Ratios of periods for tensor product motives