You can easily launch a market link or an install prompt:
Intent promptInstall = new Intent(Intent.ACTION_VIEW)
.setDataAndType(Uri.parse("file:///path/to/your.apk"),
"application/vnd.android.package-archive");
startActivity(promptInstall);
source
Intent goToMarket = new Intent(Intent.ACTION_VIEW)
.setData(Uri.parse("market://details?id=com.package.name"));
startActivity(goToMarket);
source
However, you cannot install .apks without user's explicit permission; not unless the device and your program is rooted.
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