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I don't know how it works on the web, but you can also use it on mobile.
Edit: I just tried it on the web and it looks like some sort of... non-flash interface. So some sort of javascripting involved (probably to make it harder to download? although I can easily just take a screenshot). You can click left and right or use the arrow keys left and right to navigate (it does it japanese style, so you go left to progress in pages)
A quick search turns up this app: https://play.google.com/store/apps/details?id=jp.bookwalker.kreader.android.epub
Which does allow you to read the manga straight from YenPress, the english distributor. Bad news though, you have to buy the volumes
If you're looking for a legit app that lets you support the industry, Bookwalker allows you to buy manga and light novels and read them on your smartphone.
Use Bookwalker (Google Play Store, Apple App Store). There's a "global" English version of the website and a Japanese one. If you make an account on one version of the site, you can use the same account on the other version. On the global version of the site, you can buy Japanese manga but it is a little harder to find what you're looking for. It's better to just use the Japanese version of the website.
If you install the app on your phone, you can sync the manga. The app will be the same language as your phone, but the manga will be in whatever language you purchased it in.
Here's another thing to try.
If enable the setting to "Allow installation of apps from unknown sources", you can probably just download the Bookwalker (or whatever store) app itself and install it manually.
(2) Shove it into an APK downloader site (APK is the file format for Android apps).
(3) Enable installing from unknown sources.
(4) Run APK to install said app. You might need a file manager app to find where you saved it to.