$\star$-translation for Varsovian models

The technique of $\star$-translation is important in arguments calibrating the strengths of determinacy theories against large cardinals, for example in [9] and [1] in the paper's bibliography. It has also been used in analysing the internal theory of mice, for example in [5], [3], [6]. We give a detailed development of $\star$-translation, slightly strengthening the large cardinal level in the development of [1]. We then develop a variant of $\star$-translation for Varsovian models, in which certain extenders overlapping the Woodin cardinal are total, and used to directly induce extenders on the sequence of the $\star$-translation (details for this component are missing from this draft). This variant was used in [3] and [6], where it was outlined but not developed in detail. We use the material to verify the star-translation hypothesis of [5] and deduce some self-iterability facts.