Dragan is the CEO of Milton Security and Salander's former boss. He and Salander aren't sure what to make of each other. There's a degree of attraction, and a degree of mutual respect, but also a degree of mutual mistrust. In Fire, Armansky believes, at first, that Salander is guilty of the triple murder, but that there's a reasonable explanation for her acts. To 'help' her, he launches his own investigation into the murders, offering his team to the police as consultants, but they don't get anywhere near solving the mystery. But, as facts come out, Armansky is forced to take back his guilty verdict.
For more on Armansky, see our discussion of him in The Girl With the Dragon Tattoo.