<provider
      android:name="android.support.v4.content.FileProvider"
      android:authorities="${applicationId}.file_provider"
      android:exported="false"
      android:grantUriPermissions="true">
      <meta-data
        android:name="android.support.FILE_PROVIDER_PATHS"
        android:resource="@xml/file_paths" />
    </provider>

String cachePath = (
            getExternalFilesDir("upgrade_apk") +
                File.separator +
                getPackageName() +
                ".apk");

<?xml version="1.0" encoding="utf-8"?>
<paths>
  <external-files-path name="bga_upgrade_apk" path="upgrade_apk" />
</paths>

 /**
       * 安装 apk 文件
       *
       * @param apkFile
       */
      public void installApk(File apkFile) {
        Intent installApkIntent = new Intent();
        installApkIntent.setAction(Intent.ACTION_VIEW);
        installApkIntent.addCategory(Intent.CATEGORY_DEFAULT);
        installApkIntent.setFlags(Intent.FLAG_ACTIVITY_NEW_TASK);

        if (Build.VERSION.SDK_INT > Build.VERSION_CODES.M) {
          installApkIntent.setDataAndType(FileProvider.getUriForFile(getApplicationContext(), "com.apkinstall.demo.file_provider", apkFile), "application/vnd.android.package-archive");
          installApkIntent.addFlags(Intent.FLAG_GRANT_READ_URI_PERMISSION);
        } else {
          installApkIntent.setDataAndType(Uri.fromFile(apkFile), "application/vnd.android.package-archive");
        }

        if (getPackageManager().queryIntentActivities(installApkIntent, 0).size() > 0) {
          startActivity(installApkIntent);
        }
      }