Activist investment management firm and hedge fund operator Elliott Management has apparently built up a substantial stake in Deutsche Telekom AG (DTEGY). Along with that stake in the telecommunications company, the firm has also signaled to Deutsche Telekom to not entertain a proposed $300 billion merger deal with its U.S. arm, T-Mobile US (TMUS). Instead, Elliott wants the telecom major to explore other avenues of increasing shareholder value, including share repurchases. Let's take a closer look.