Healthcare is important. Asgardia could, as an independent state, unite researchers worldwide. It would be possible to share knowledge, work in a multidisciplinar team with people all over the world, but without the boundaries of country borders. Asgardia would provide a platform for discussion.

What do you think: how could Asgardia improve research and healthcare internationally?

I honestly can not posit a reason why not.  For example, one of the common problems in space is bone loss.  If in space we can conquer that problem just think of the implications for osteoporosis on Earth.