Glitch with google chrome when downloading files

You're suffering from this bug, I think. Judging by the fact that it's almost five years old and the amount of attention it's gotten from the devs, I wouldn't bet on it being fixed anytime soon (and even then only on new devices, probably).

In short: the download manager rejects your SSL certificate because it doesn't trust it, and, unlike the browser, can't be bothered to ask the user for confirmation.

These are your options (and all of them suck):

1. Manually import the certificate into the Android trust store. A step by step explanation of it can be found here, for instance.

2. Use a different browser and/or download manager. I see this issue on both the stock browser and Chrome, but reportedly Firefox doesn't suffer from it.

3. Serve your download over HTTP. This sort of defeats the purpose of having a secure connection in the first place, of course, but if the contents of the download aren't that touchy, this might be the most painless way to go, from a usability perspective.

Obviously numbers one and two are ridiculous to expect of your users, so unless you can drop down to HTTP, I'm afraid you're out of luck.