I assume you want to start a new activity and open the new APK, so you have to start an Intent
to open the new application
// Here filePath is the Path for the .apk
Java.IO.File a = new Java.IO.File (filePath);
Intent intent = new Intent(Intent.ActionView);
intent.SetDataAndType(global::Android.Net.Uri.FromFile(new Java.IO.File(filePath)), "application/vnd.android.package-archive");
intent.SetFlags(ActivityFlags.NewTask | ActivityFlags.ClearTask);
try
{
var c = Android.App.Application.Context;
c.StartActivity(intent);
dialog.Dismiss();
this.Finish();
}
catch (Exception e)
{
}