• Patients must have received allogeneic HSCT and be greater than 30 days post-HSCT at the time of registration.

• Patients must have evidence of documented HAdV infection/reactivation. Patients may be:

‣ Symptomatic with any detectable viral load OR

⁃ Asymptomatic with viral load that is:

∙ \>1000 copies/ml in peripheral blood OR qualitative detection in stool, urine and/or other specimens

• Patients must have poor response and/or contraindication to therapy:

‣ Absence of an improvement of viral load (decrease by at least 1 log, i.e. 10-fold) after ≥ 14 days of antiviral therapy with ganciclovir, valganciclovir and/or foscarnet. OR

⁃ New, persistent and/or worsening HAdV-related symptoms, signs and/or markers of end organ compromise while on antiviral therapy with ganciclovir, valganciclovir or foscarnet. OR

⁃ Have contraindications or experience adverse effects of antiviral therapy with ganciclovir, valganciclovir, cidofovir or foscarnet.

• Performance Score: Eastern Cooperative Oncology Group (ECOG) Performance Score ≤ 3. Karnofsky (≥ 16 years) or Lansky (\<16 years) performance score ≥ 50

• The effects of virus-specific, antigen-selected T cells on the developing human fetus are unknown. For this reason, women of child-bearing potential and men must agree to use adequate contraception (double barrier method of birth control or abstinence) 4 weeks prior to study entry, for the duration of study participation and for 3 months after completing treatment.

• Subjects who are 14 years and older must have the ability to understand and the willingness to sign a written informed consent document, or assent document.