A multi-functional helper ingredient that's used mainly as a pigment carrier. The pigment can be an inorganic sunscreen (such as titanium dioxide) or a colorant that is blended with alumina platelets and then often coated with some kind of silicone (such as triethoxycaprylylsilane). This special treatment enables pigments to be evenly dispersed in the formula and to be spread out easily and evenly upon application. It is super useful both for mineral sunscreens as well as for makeup products.
Other than that, alumina can also be used as an absorbent (sometimes combined with the mattifying powder called polymethylsilsesquioxane), a viscosity controlling or an opacifying (reduces the transparency of the formula) agent.