This is Richard K. Morgan's Altered Carbon:
Excerpts from the Wiki description hit most of the major points you identify:
In the novel's somewhat dystopian world, human personalities can be stored digitally and downloaded into new bodies, called sleeves. Most people have cortical stacks in their spinal columns that store their memories. If their body dies, their stack can be stored indefinitely.
While most people can afford to get resleeved at the end of their lives, they are unable to update their bodies and most go through the full ageing process each time which discourages most from resleeving more than once or twice. So while normal people can live indefinitely in theory, most choose not to. Only the wealthy are able to acquire replacement bodies on a continual basis. The long-lived are called Meths, a reference to the Biblical figure Methuselah. The very rich are also able to keep copies of their minds in remote storage, which they update regularly. This ensures that even if their stack is destroyed, they can be resleeved.
The plot involves a murder mystery, one of these rich people trying to figure out who murdered... himself, in a previous body.
Kovacs is an ex-Envoy, a military unit formed to cope with the challenge of interstellar warfare. Faster-than-light travel is only possible by subspace transmission, called needlecasting, of a digitally stored consciousness to "download centers" where resleeving into physical bodies can be carried out. Transmitting normal soldiers in this way would severely inhibit their effectiveness, since they would have to cope with a new body and an unknown environment while fighting
Kovacs, killed in the novel's prologue and stored in digital form, is downloaded into a sleeve formerly inhabited by Bay City (formerly San Francisco) policeman Elias Ryker. The plot unfolds through Kovacs' narrative. Kovacs eventually solves the mystery, but only after a great deal of violence, including torture in virtual reality, which he is able to bear only because of his Envoy training.
These parts cover the "interstellar empire" aspects and the main character who gets a new body at the start of the book, and the "a great deal of violence" part. I can also confirm they do change bodies over the course of the book, and although I can't personally recall a fight in a biodome-type structure, that's easily possible... I recall a lot of fights, it's the settings of those fights that didn't stick with me.