The short answer is: she's not.
The long answer is that over the course of several commissions, her hair became lighter and lighter, eventually growing a bit of a reddish tint. I know there's a couple pictures I use over and over as reference, and I think artists are just using those to pick the color. There's definitely a few where I'd say Invy looks like a redhead, though. So lets go way back. Way way way back when Invy was still a character in a superhero game, and when I would describe her personality people would tell me "she's not a very good superhero" to which I'd reply "yeah? Good, she's not." That's a story for another day, anyway, check out the original

She's definitely got some dark brown hair in this. I don't think you could use the word "red" to describe it, but maybe I'm dumb. Most of the early art has her in a similar hair color, or a little bit lighter. These ones tint it up a little


Still brown though? Yeah, I'm not too sure where the red came in. Heck, you've even got some really great pieces with her in dark brown hair
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I think I can pinpoint where it all started to change, though. Around 2011 I wanted to shift my characters a bit more out of the superhero scene. At the very least I wanted to give them a bit more personality and some civilian clothes. Invy was the first one to change. She was supposed to like robots and technology stuff (she had a weird armored suit and teleportation devices), and she already had personality of being shy, liking video games, nonviolent, etc, so she got some normal clothes
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She came out fantastic, pretty much exactly how I wanted. Looking back, though, the hair is significantly lighter. Which is fine! It was definitely brown, you could say the lighting in the others made it look different, but still a good color on her, I like it. So much so that this became my go-to reference picture for a while, sometimes it still is. The only thing about it is that after this point, the darker colored hairs fall significantly out of favor. Yes, if you check her folder, there's definitely some darker ones. There's a few where she may have some redder tones

I don't think I'd call her a redhead in these. Maybe I'm dumb, or I'm just blind because of the slow shift. Keep in mind, these are also top pick-these-for-reference images that I give to artists. They're decent colors, I like her with a lighter brown shade more than the dark, honestly. If you want red, I'd say these are the reddest (especially the first one, haha)

And that's still fine. Not every picture has to get stuff exactly correct. The one on the left could be a bright sunshine day and everything just looks brighter and redder. I do know that artist loves summer, but in contrast I think he said something about her being a redhead and I never corrected him, haha. That's sort of the evolution of her becoming a redhead, and she's really not supposed to be. Also keep in mind that for the cosplay, I picked the color for her hair and I believe it was labeled "chocolate." Could be wrong

And this isn't trying to bash on anyone or anything, I love all the pictures I've set as an example here, and all of the ones that I haven't. If I had a problem with the colors, I'd ask for a change. And believe me, I have asked for pretty much an entire picture's colors to be changed before (when the artist said it was simple to do) so there's no issue there. Honestly, it never bothered me until someone asked me that question. Going forward, I might make more of an effort to stress that she has brown hair, but other than that, whatever happens will happen. Invy has brown hair, sometimes it gets a red tint depending on the lighting. Simple as that? Maybe. We'll see
If you wanna see more of the varying hair colors, I encourage you to check out her folder and show all the artists some love
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