Inclusion Criteria:

• * Biopsy proven cutaneous squamous cell carcinoma which is locally advanced
• * Mixed histology tumors that are predominantly squamous cell carcinoma are eligible
• * Locally advanced primary tumor is T3-T4 and/or N+ by AJCC and/or UICC 8th edition clinical criteria
• * T3-T4 primary tumor characteristics noted below:
• * Non-eyelid tumor \>4 cm in maximum dimension or with bone erosion or invasion, perineural invasion of nerve 0.1 mm or larger, or invasion beyond subcutaneous fat or \>6 mm from granular layer of adjacent normal epidermis
• * Eyelid tumor \>2 cm or invading adjacent ocular, orbital or facial structures
• * ≥18 years old
• * Unresectable or medically inoperable according to local multidisciplinary consensus for reasons such as:
• * Tumor or regional lymph node metastases that has recurred despite ≥2 prior surgical procedures, with another curative resection unlikely
• * Tumor or nodal disease with significant local invasion that precludes complete resection
• * Tumor or nodal disease in anatomically challenging area where surgery may result in significant disfigurement or dysfunction (amputation of nose, ear, eye, digit, limb, etc)
• * Medical contraindication to surgery
• * Patient refusal of surgery due to anticipate morbidity
• * ECOG ≤2
• * Adequate bone marrow and metabolic function (by blood tests)
• * Total bilirubin ≤1.5 x upper limit of normal
• * Aspirate aminotransferase (AST) ≤3 x upper limit of normal
• * Alanine aminotransferase (ALT) ≤3 x upper limit of normal
• * Alkaline phosphatase ≤2.5 x upper limit of normal
• * Serum creatinine ≤1.5 x upper limit of normal or estimated creatinine clearance \>30 mL/min according to Cockcroft-Gault formula
• * Hemoglobin \>9 g/dL
• * Absolute neutrophil count ≥1.5 x10\^9/L
• * Platelet count ≥75 x10\^9/L
• * Able to provide informed consent
• * Acceptable candidate for curative intent radiotherapy and Cemiplimab immunotherapy, in opinion of radiation and medical oncologist, respectively
• * Life expectancy \>18 months

Exclusion Criteria:

• * Primary tumor originating on the mucosal (non-hair bearing) lip or nose, anogenital (penis, scrotum, vulva, perianal) area
• * Iatrogenic immunosuppression (\>prednisone 10 mg/day or equivalent within 14 days of initiation of treatment)
• * Women of child bearing potential unwilling or unable to use effective contraception while receiving treatment with cemiplimab and for 4 months thereafter
• * Distant metastases
• * Clinically significant autoimmune disease that requires iatrogenic immunosuppression
• o For example, severe rheumatoid arthritis requiring disease modifying antirheumatic drugs, such as methotrexate
• * Current or previous hematopoietic malignancy (leukemia, lymphoma)
• * Prior allogeneic transplant of solid organ or bone marrow
• * Concurrent malignancies with \>10% risk of metastasis or death within 2 years
• * Prior aPD1 immunotherapy or PI3Kδ inhibitor use
• * Prior radiotherapy for the cutaneous squamous cell carcinoma requiring treatment
• * Other ongoing cancer therapy
• o Adjuvant endocrine therapy is permitted for patients with prostate or breast cancer
• * Uncontrolled HIV or infectious hepatitis (viral load detectable in patient with known infection)
• * Pregnancy or breastfeeding
• * Comorbid or diagnostic abnormalities within the last year that would interfere with interpretation of study results