Determinacy transfer theorems play an important role in the descriptive set theoretic and inner model theoretic study of pointclasses. We prove that determinacy for $\sigma$-projective sets, a natural generalization of projective sets to a $\sigma$-algebra, of length $\omega$ implies the determinacy of a large class of games of length $\omega^2$. The proof of this result involves inner models with large cardinals and in the process, we obtain a new proof of $\sigma$-projective determinacy for games of countable length from the existence of inner models with large cardinals.

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