Mutant KRAS G12V-specific TCR Transduced T Cell Therapy for Advanced Pancreatic Cancer

Inclusion Criteria: * Patients with measurable and pathologically confirmed advanced pancreatic cancer, including metastatic pancreatic cancer (who have received standard chemotherapy) and recurrent pancreatic cancer (who have received surgery and adjuvant chemotherapy previously). * Patient's tumor must express the KRAS G12V mutation, or a G12V mutation in HRAS or NRAS, as determined by DNA or RNA sequencing methods. * Patients must be HLA-A\*11:01. * Patients with brain metastasis may be eligible if they are asymptomatic and there are fewer than 3 brain lesions that are each less than 1 cm in diameter. * Patients between 18 to 75 years old are eligible. * Patients should have good clinical performance status (ECOG 0 or 1). * Patients must practice birth control once enrolled into the study and for up to four months after therapy. * Patients must be seronegative for HIV antibody. * Patients must be seronegative for hepatitis B surface antigen and core antibody (or HBV non-detectable by QPCR). * Patients must be seronegative for hepatitis C antibody (or HCV non-detectable by QPCR). * Baseline hematology criteria: * Absolute neutrophil count of at least 1000/mm\^3. * White blood cell count of at least 3000/mm\^3. * Platelet count of at least 100,000/mm\^3. * Hemoglobin \> 8.0 g/dL. * Baseline chemistry criteria: * Serum ALT/AST less than or equal to 3.0 x ULN. * Total bilirubin less than or equal to 1.5 mg/dL, unless the patient has Gilbert's Syndrome in which case total bilirubin must be less than or equal to 3.0 mg/dL. * Serum creatinine less than or equal to 1.6 mg/dL. * Anticipated lifespan greater than 12 weeks. * Patients must be willing and able to comply with all study-related procedures and follow-up requirements. * Patients must be able to understand and sign a written Informed Consent Document as well as a durable power of attorney. Exclusion Criteria: * Women who are pregnant or breastfeeding. * Patients with any form of primary immunodeficiency (such as Severe Combined Immunodeficiency Disease or HIV). * Patients with active systemic infections, coagulation disorders, or any other major medical illnesses. * Patients with concurrent opportunistic infections. * Patients on concurrent systemic steroid therapy. * Patients with a history of severe immediate hypersensitivity reaction to any of the medicines used in this study (e.g., cyclophosphamide, fludarabine). * Patients with active coronary ischemic symptoms. * Patients who are receiving any other investigational agents.