Internationally disaggregated headquarters arise from cross‐border relocations of headquarters components. To shed more light on the business consequences of such component relocations, we analyse stock market reactions to inversion initiatives, which are plans by US firms to offshore their registered seat. Combining business economics and institutional theory, we develop an explanatory framework centred on repatriation taxes on foreign income. Since inversions enable US firms to free themselves from such taxes in the US, we hypothesize that inversions by firms that face higher US tax costs in repatriating income will be received more positively by investors, and especially so if the inversion's destination country has no repatriation tax. Yet by freeing themselves from US repatriation taxes, inverting firms deprive the US government of tax revenues and will therefore likely lose legitimacy among US officials. The risks associated with losing such legitimacy, we argue, are higher for firms that are more dependent on the US government, causing the relationship between the US tax costs of repatriating income and investor reactions to inversions to be less positive for such firms. We find substantial support for our framework in an event study of up to 117 inversions announced over the period 1990–2016. Our findings argue for a nuanced, contingency view of the business consequences of inverting and suggest that legitimacy losses are not always as hazardous as previously thought.