PPSSPP is a PSP emulator for Android and other platforms. It runs a lot of games, but depending on the power of your device all may not run at full speed.
Please note that ARMv6-based devices may have various kinds of issues, and more modern devices are recommended.
See http://www.ppsspp.org for more information.
No games are included with this download, you will have to dump your own PSP games and turn them into .ISO or .CSO files, or simply play free homebrew games, which are available online. Put those in /PSP/GAME on your SD card / USB storage.
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