Electric System Problem- '04 XC70

[Docmphd]

My 2004 XC70 started experiencing some problems recently. I'm not sure if the problem is the regulator, the alternator, or something else like a belt.

On Thursday, the batter light came on and the dash message said "EL SYSTEM SERVICE REQUIRED"
Battery light stayed on during the remainder of the drive, another 45 minutes.

On Friday, with the battery light still on....the ABS light went on, as did the airbag light, then the A/C shut off, followed by the radio shutting off. Couldn't even roll up the windows. Turned the car off when I got home, then a few hours later I jumped it to roll up the windows and re-park for the night.

Saturday, thought I'd have to jump the car to start it, but tried a cold start without jump and it started just fine. The battery light was OFF, no message, no errors of any kind. AC worked, radio worked, nothing out of the ordinary. Drove the car around the neighborhood and it was fine for about 5 minutes, then the batter light came on, with dash message "EL SYSTEM SERVICE REQUIRED." Then, just like Thursday, systems started shutting down.

So, is it an alternator? The regulator on the alternator? Maybe the belt (since it was fine cold)? Something else? Local tire/battery shop said the battery was fine (they installed it about 3 months ago) and said it was likely the alternator.

UPDATE: I tested my theory that this issue only appears after the car warms up. I turned it off after the last drive (mentioned above), and let it sit for 4 hours. Turned it on, no warnings/lights/errors.