Aye Cristobal, welcome to the forum.
I have never had, or worked on an XBR, but there are many on here who have, so hopefully they will be able to help.
From your decsription the fault sounds very similar to one that I have been having with a Moto Morini 125H. The engine readily starts and will tick over between 1,100 - 1,200 rpm for a long time. BUT, if you try to increase the engine speed (revs) above 2,000 - 2,500 rpm when the ignition would start to advance, there is a lot of stuttering and then the engine cuts out. With my Morini this is being caused by the ignition not being advanced by the CDI, from the trigger coil signal. Spares are unobtainable for the Morini, but this is not the case for the XBR, so far as I am aware.
So, I would suggest that if possible, you test the CDI, timing trigger coil, and ignition coil to see if they are all functioning correctly. I do not know what the test procedures and values are for the XBR components and others should be able to help advise with this.
Do you have a Honda Owners manual?
And may I ask if you are resident in the UK or elsewhere, it helps with replies, if you are asking for spares information in your country.
I hope that you can sort the problem out and get to enjoy riding the XBR, as that is what we all enjoy.
Good health, Bill