Is possible to programmatically install a dynamically downloaded apk from a custom Android application.
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);
Intent goToMarket = new Intent(Intent.ACTION_VIEW)
.setData(Uri.parse("market://details?id=com.package.name"));
startActivity(goToMarket);
However, you cannot install .apks without user's explicit permission; not unless the device and your program is rooted.